Compressor stator vane airfoils

ABSTRACT

A stator vane includes an airfoil having an airfoil shape. The airfoil shape has a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in one of TABLE I or TABLE II. The Cartesian coordinate values of X, Y, and Z are defined relative to a point data origin at a base of the airfoil. The Cartesian coordinate values of X, Y, and Z are non-dimensional values that are convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y, and Z by a scaling factor of the airfoil in the unit of distance. The X and Y values are connected by smooth continuing arcs to define airfoil profile sections at each Z value. The airfoil profile sections at Z values are joined smoothly with one another to form a complete airfoil shape.

FIELD

The present disclosure relates to an airfoil for a compressor statorvane disposed within a stage of a compressor section of a land-based gasturbine system and, more particularly, relates to a shape defining aprofile for an airfoil of a compressor stator vane.

BACKGROUND

Some simple cycle or combined cycle power plant systems employturbomachines in their design and operation. Generally, turbomachinesemploy airfoils (e.g., stator vanes or nozzles and rotor blades), whichduring operation are exposed to fluid flows. These airfoils areconfigured to aerodynamically interact with the fluid flows and totransfer energy to or from these fluid flows as part of powergeneration. For example, the airfoils may be used to compress fluid, tocreate thrust, to convert kinetic energy to mechanical energy, and/or toconvert thermal energy to mechanical energy. As a result of theseinteractions and conversions, the aerodynamic characteristics of theseairfoils may result in losses that have an impact on system and turbineoperation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages of the stator vanes and turbomachines inaccordance with the present disclosure will be set forth in part in thefollowing description, or may be obvious from the description, or may belearned through practice of the technology.

In accordance with one embodiment, a stator vane is provided. A statorvane includes an airfoil having an airfoil shape. The airfoil shape hasa nominal profile substantially in accordance with Cartesian coordinatevalues of X, Y, and Z set forth in one of TABLE I or TABLE II. TheCartesian coordinate values of X, Y, and Z are defined relative to apoint data origin at a base of the airfoil. The Cartesian coordinatevalues of X, Y, and Z are non-dimensional values that are convertible todimensional distances expressed in a unit of distance by multiplying theCartesian coordinate values of X, Y, and Z by a scaling factor of theairfoil in the unit of distance. The X and Y values are connected bysmooth continuing arcs to define airfoil profile sections at each Zvalue. The airfoil profile sections at Z values are joined smoothly withone another to form a complete airfoil shape.

In accordance with another embodiment, a stator vane is provided. Thestator vane includes an airfoil having a nominal suction-side profilesubstantially in accordance with suction-side Cartesian coordinatevalues of X, Y, and Z set forth in one of TABLE I or TABLE II. TheCartesian coordinate values of X, Y, and Z are defined relative to apoint data origin at a base of the airfoil. The Cartesian coordinatevalues of X, Y, and Z are non-dimensional values that are convertible todimensional distances expressed in a unit of distance by multiplying theCartesian coordinate values of X, Y, and Z by a scaling factor of theairfoil in the unit of distance. The X and Y values are connected bysmooth continuing arcs to define suction-side profile sections at each Zvalue. The suction-side profile sections at the Z values are joinedsmoothly with one another to form a complete airfoil suction-side shape.

In accordance with yet another embodiment, a turbomachine is provided.The turbomachine includes a compressor section, a turbine sectiondownstream from the compressor section, and a combustion sectiondownstream from the compressor section and upstream from the turbinesection. A stator vane is disposed within one of the compressor sectionor the turbine section. The stator vane includes an airfoil having anairfoil shape. The airfoil shape has a nominal profile substantially inaccordance with Cartesian coordinate values of X, Y, and Z set forth inone of TABLE I or TABLE II. The Cartesian coordinate values of X, Y, andZ are defined relative to a point data origin at a base of the airfoil.The Cartesian coordinate values of X, Y, and Z are non-dimensionalvalues that are convertible to dimensional distances expressed in a unitof distance by multiplying the Cartesian coordinate values of X, Y, andZ by a scaling factor of the airfoil in the unit of distance. The X andY values are connected by smooth continuing arcs to define airfoilprofile sections at each Z value. The airfoil profile sections at Zvalues are joined smoothly with one another to form a complete airfoilshape.

These and other features, aspects and advantages of the present statorvanes and turbomachines will become better understood with reference tothe following description and appended claims. The accompanyingdrawings, which are incorporated in and constitute a part of thisspecification, illustrate embodiments of the technology and, togetherwith the description, serve to explain the principles of the technology.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present stator vanes andturbomachines, including the best mode of making and using the presentsystems and methods, directed to one of ordinary skill in the art, isset forth in the specification, which makes reference to the appendedfigures, in which:

FIG. 1 is a schematic illustration of a turbomachine in accordance withembodiments of the present disclosure;

FIG. 2 illustrates a cross-sectional side view of a compressor section(e.g., of the turbomachine of FIG. 1 ), in accordance with embodimentsof the present disclosure;

FIG. 3 illustrates a perspective view of a stator vane as may be used inthe compressor section of FIG. 2 , in accordance with embodiments of thepresent disclosure;

FIG. 4 illustrates an airfoil profile section of an airfoil from alongthe line 4-4 shown in FIG. 3 , in accordance with embodiments of thepresent disclosure;

FIG. 5 illustrates a graph of a stagger angle distribution belonging toan airfoil disposed on a stator vane within a specified stage of acompressor section, in accordance with embodiments of the presentdisclosure; and

FIG. 6 illustrates a graph of a stagger angle distribution belonging toan airfoil disposed on a stator vane within a specified stage of acompressor section, in accordance with embodiments of the presentdisclosure.

DETAILED DESCRIPTION

Reference now will be made in detail to embodiments of the presentstator vanes and turbomachines, one or more examples of which areillustrated in the drawings. Each example is provided by way ofexplanation, rather than limitation of, the technology. In fact, it willbe apparent to those skilled in the art that modifications andvariations can be made in the present technology without departing fromthe scope or spirit of the claimed technology. For instance, featuresillustrated or described as part of one embodiment can be used withanother embodiment to yield a still further embodiment. Thus, it isintended that the present disclosure covers such modifications andvariations as come within the scope of the appended claims and theirequivalents.

The detailed description uses numerical and letter designations to referto features in the drawings. Like or similar designations in thedrawings and description have been used to refer to like or similarparts of the invention. As used herein, the terms “first”, “second”, and“third” may be used interchangeably to distinguish one component fromanother and are not intended to signify location or importance of theindividual components.

As used herein, the terms “upstream” (or “forward”) and “downstream” (or“aft”) refer to the relative direction with respect to fluid flow in afluid pathway. For example, “upstream” refers to the direction fromwhich the fluid flows, and “downstream” refers to the direction to whichthe fluid flows. The term “radially” refers to the relative directionthat is substantially perpendicular to an axial centerline of aparticular component, the term “axially” refers to the relativedirection that is substantially parallel and/or coaxially aligned to anaxial centerline of a particular component, and the term“circumferentially” refers to the relative direction that extends aroundthe axial centerline of a particular component.

Terms of approximation, such as “generally,” “substantially,” or “about”include values within ten percent greater or less than the stated value.When used in the context of an angle or direction, such terms includewithin ten degrees greater or less than the stated angle or direction.For example, “generally vertical” includes directions within ten degreesof vertical in any direction, e.g., clockwise or counter-clockwise.

Referring now to the drawings, FIG. 1 illustrates a schematic diagram ofone embodiment of a turbomachine, which in the illustrated embodiment isa gas turbine 10. Although an industrial or land-based gas turbine isshown and described herein, the present disclosure is not limited to anindustrial and/or land-based gas turbine unless otherwise specified inthe claims. For example, the stator vane airfoils as described hereinmay be used in any type of turbomachine including but not limited to asteam turbine, an aircraft gas turbine, or a marine gas turbine.

As shown, gas turbine 10 generally includes an inlet section 12, acompressor section 14 disposed downstream of the inlet section 12, oneor more combustors (not shown) within a combustor section 16 disposeddownstream of the compressor section 14, a turbine section 18 disposeddownstream of the combustor section 16, and an exhaust section 20disposed downstream of the turbine section 18. Additionally, the gasturbine 10 may include one or more shafts 22 coupled between thecompressor section 14 and the turbine section 18.

The multi-stage axial compressor section or compressor section 14 maygenerally include a plurality of rotor disks 24 (one of which is shown)and a plurality of rotor blades 44 extending radially outwardly from andconnected to each rotor disk 24. Each rotor disk 24 in turn may becoupled to or form a portion of the shaft 22 that extends through thecompressor section 14. The compressor section 14 may further include oneor more stator vanes 50 arranged circumferentially around the shaft 22.The stator vanes 50 may be fixed to a static casing or compressor casing48 that extends circumferentially around the rotor blades 44.

The turbine section 18 may generally include a plurality of rotor disks28 (one of which is shown) and a plurality of rotor blades 30 extendingradially outwardly from and being interconnected to each rotor disk 28.Each rotor disk 28 in turn may be coupled to or form a portion of theshaft 22 that extends through the turbine section 18. The turbinesection 18 further includes a turbine casing 33 that circumferentiallysurrounds the turbine portion of the shaft 22 and the rotor blades 30,thereby at least partially defining a hot gas path 32 through theturbine section 18. The turbine casing 33 may be configured to support aplurality of stages of stationary nozzles 29 extending radially inwardlyfrom the inner circumference of the turbine casing 33.

During operation, a working fluid such as air flows through the inletsection 12 and into the compressor section 14 where the air isprogressively compressed, thus providing pressurized air to thecombustor(s) of the combustor section 16. The pressurized air is mixedwith fuel and burned within the combustor(s) to produce combustion gases34. The combustion gases 34 flow through the hot gas path 32 from thecombustor section 16 into the turbine section 18, wherein energy(kinetic and/or thermal) is transferred from the combustion gases 34 tothe rotor blades 30, causing the shaft 22 to rotate. The mechanicalrotational energy may then be used to power the compressor section 14and/or to generate electricity. The spent combustion gases 34 exitingthe turbine section 18 (sometimes referred to as “flue gases” or“exhaust gases”) may then be exhausted from the gas turbine 10 via theexhaust section 20.

FIG. 2 illustrates a cross-sectional side view of an embodiment of thecompressor section 14 of the gas turbine 10 of FIG. 1 , which is shownas a multi-stage axial compressor section 14, in accordance withembodiments of the present disclosure. As shown in FIGS. 1 and 2 , thegas turbine 10 may define a cylindrical coordinate system. Thecylindrical coordinate system may define an axial direction A (e.g.,downstream direction) parallel to and/or along an axial centerline 23 ofthe gas turbine 10, a radial direction R perpendicular to the axialcenterline 23, and a circumferential direction C extending around theaxial centerline 23.

In operation, air 15 may enter the compressor section 14 in the axialdirection A through the inlet section 12 and may be pressurized in themulti-stage axial compressor section 14. The compressed air may then bemixed with fuel for combustion within the combustor section 16 to drivethe turbine section 18, which rotates the shaft 22 in thecircumferential direction C and, thus, the multi-stage axial compressorsection 14. The rotation of the shaft 22 also causes one or more rotorblades 44 (e.g., compressor rotor blades) within the multi-stage axialcompressor section 14 to draw in and pressurize the air received by theinlet section 12.

The multi-stage axial compressor section 14 may include a rotor assembly46 having a plurality of rotor disks 24. Rotor blades 44 may extendradially outward from the rotor disks 24. The entire rotor assembly 46(e.g., rotor disks 24 and rotor blades 44) may rotate in thecircumferential direction C during operation of the gas turbine 10. Therotor assembly 46 may be surrounded by a compressor casing 48. Thecompressor casing may be static or stationary, such that the rotorassembly 46 rotates relative to the compressor casing 48. Stator vanes50 (e.g., variable stator vanes and/or fixed stator vanes) may extendradially inward from the compressor casing 48.

As shown in FIG. 2 , one or more stages of the stator vanes 50 may bevariable stator vanes 51, such that an angle of the stator vane 50 maybe selectively actuated (e.g., by a controller 200). For example, in theembodiments shown in FIG. 2 , the first two stages of the compressorsection 14 (e.g., S1 and S2) may include variable stator vanes 51. Inmany embodiments, as shown, the rotor blades 44 and stator vanes 50 maybe arranged in stages in an alternating fashion, such that most stagesof the rotor blades 44 are disposed between two stages of stator vanes50 in the axial direction A.

In some embodiments, the compressor casing 48 of the compressor section14 or the inlet section 12 may have one or more sets of inlet guidevanes 52 (IGVs) (e.g., variable IGV stator vanes). The inlet guide vanes52 may be mounted to the compressor casing 48, may be spaced apart fromone another in the circumferential direction C, and may be operable tocontrol the amount of air 15 that enters the compressor section 14.Additionally, an outlet 56 of the compressor section 14 may have a setof outlet guide vanes 58 (OGVs). The OGVs 58 may be mounted to thecompressor casing 48, may be spaced apart from one another in thecircumferential direction C, and may be operable to control the amountof air 15 that exits the compressor section 14.

In exemplary embodiments, as shown in FIG. 2 , the variable stator vanes51 and the IGVs 52 may each be configured to vary its vane anglerelative to the gas flow (e.g., air flow) by rotating the vane 51, 52about an axis of rotation (e.g., about the radially oriented vaneshaft). However, each variable stator vane 51 (including the IGVs 52)may be otherwise stationary relative to the rotor blades 44. In certainembodiments, the variable stator vanes 51 and the IGVs 52 may be coupledto an actuator 19 (e.g., electric drive, pneumatic drive, or hydraulicdrive). The actuators 19 may be in operable communication (e.g.,electrical communication) with a controller 200. The controller 200 maybe operable to selectively vary the vane angle. In other embodiments,all of the stator vanes 50 may be fixed, such that the stator vanes 50are configured to remain in a fixed angular position (e.g., the vaneangle does not vary).

The compressor section 14 may include a plurality of rows or stagesarranged in a serial flow order, such as between 2 to 30, 2 to 25, 2 to22, 2 to 14, or 2 to 10 rows or stages, or any specific number or rangetherebetween. Each stage may include a plurality of rotor blades 44(attached to rotor disks 24 and circumferentially spaced about the axialcenterline 23) and a plurality of stator vanes 50 (attached to thecompressor casing 48 and circumferentially spaced about the axialcenterline 23). In each stage, the multi-stage axial compressor section14 may include 2 to 1000, 5 to 500, or 10 to 100 of circumferentiallyarranged rotor blades 44, and 2 to 1000, 5 to 500, or 10 to 100 ofcircumferentially arranged stator vanes 50. In particular, theillustrated embodiment of the multi-stage axial compressor section 14includes 22 stages (e.g., S1-S22).

It may be appreciated that each stage has a set of rotor blades 44disposed at a first axial position and a set of stator vanes 50 disposedat a second axial position along the length of the compressor section14. In other words, each stage has the rotor blades 44 and stator vanes50 axially offset from one another, such that the compressor section 14has an alternating arrangement of rotor blades 44 and stator vanes 50one set after another along the length of the compressor section 14.Each set of rotor blades 44 extends (e.g., in a spaced arrangement) inthe circumferential direction C about the shaft 22, and each set ofstator vanes 50 extends (e.g., in a spaced arrangement) in thecircumferential direction C within the compressor casing 48.

While the compressor section 14 may include greater or fewer stages thanare illustrated, FIG. 2 illustrates an embodiment of the compressorsection 14 having twenty two stages arranged in a serial flow order andidentified as follows: first stage S1, second stage S2, third stage S3,fourth stage S4, fifth stage S5, sixth stage S6, seventh stage S7,eighth stage S8, ninth stage S9, tenth stage S10, eleventh stage S11,twelfth stage S12, thirteenth stage S13, fourteenth stage S14, fifteenthstage S15, sixteenth stage S16, seventeenth stage S17, eighteenth stageS18, nineteenth stage S19, twentieth stage S20, twenty-first stage S21,and twenty-second stage S22. The IGVs 52 are upstream (i.e., forward) offirst stage S1, and the OGVs 58 are downstream (i.e., aft) of thetwenty-second stage S22.

In certain embodiments, each stage may include rotor blades 44 andstator vanes 50 (e.g., fixed stator vanes 50 and/or variable statorvanes 51). As used herein, a rotor blade 44 disposed within one of thesections S1-S22 of the compressor section 14 may be referred to bywhichever stage it is disposed within, e.g., “a first stage compressorrotor blade,” “a second stage compressor rotor blade,” “a third stagecompressor rotor blade,” etc. Similarly, a stator vane 50 disposedwithin one of the sections S1-S22 of the compressor section 14 may bereferred to by whichever stage it is disposed within, e.g., “a thirdstage compressor stator vane,” “a fourth stage compressor stator vane,”“a fifth stage compressor stator vane,” etc.

In use, the rotor blades 44 may rotate circumferentially about the axialcenterline 23 within the compressor casing 48 and between the statorvanes 50. Rotation of the rotor blades 44 may result in air entering theinlet section 12. The air is then subsequently compressed as ittraverses the various stages (e.g., first stage S1 to twenty-secondstage S22) of the compressor section 14 and moves in the axial directiondownstream of the multi-stage axial compressor section 14. Thecompressed air may then exit through the outlet 56 of the multi-stageaxial compressor section 14. As discussed above, the outlet 56 may havea set of outlet guide vanes 58 (OGVs). The compressed air that exits thecompressor section 14 may be directed to the combustor section 16 andmixed with fuel for combustion. Air from one or more stages of thecompressor section 14 may also be directed to the turbine section 18 orelsewhere in the gas turbine 10 for cooling and/or sealing.

The IGV 52, the stages (e.g., S1-S22) of rotor blades 44 and statorvanes 50, and the OGV 58 of the compressor section 14 may be groupedinto one or more sections or portions of the compressor section 14 forreference purposes. For the purposes of the grouping, portions thecompressor section 14 may be expressed in terms of a percentage, such asa percentage of the compressor section 14 from the inlet (e.g., 0% ofthe compressor section 14) to the outlet (e.g., 100% of the compressorsection 14) in the axial or downstream direction. In this way, thecompressor section 14 may include, in a serial flow order, an earlystage 60, a mid stage 62, and a late stage 64. In particular, the earlystage 60 may include from approximately 0% to approximately 25% of thecompressor section 14 (e.g., from the IGV 52 to about the sixth stageS6). The mid stage 62 may include from approximately 25% toapproximately 75% of the compressor section 14 (e.g., from about theseventh stage S7 to about the eighteenth stage S18). The late stage 64may include from approximately 75% to approximately 100% of thecompressor section 14 (e.g., from about the nineteenth stage S19 to theOGV 58).

Accordingly, the Cartesian coordinate data contained within each ofTABLES I and 11 may correspond to an airfoil shape of an airfoil 100disposed within the mid stage 62 of the compressor section 14.Particularly, the Cartesian coordinate data contained within each ofTABLES I and II may correspond to an airfoil shape of an airfoil 100disposed within the last two stages of the mid stage 62 (e.g., theseventeenth stage S17 and the eighteenth stage S18).

For example, in exemplary embodiments, the Cartesian coordinate datacontained within TABLE I may correspond to an airfoil shape of anairfoil 100 disposed on a stator vane 50 within the seventeenth stageS17 of the compressor section 14. The Cartesian coordinate datacontained within TABLE II may correspond to an airfoil shape of anairfoil 100 disposed on a stator vane 50 within the eighteenth stage S18of the compressor section 14.

However, in various other embodiments, each of TABLES I and II maycontain Cartesian coordinate data of an airfoil shape of an airfoil 100that may be disposed on a stator vane 50 or rotor blade 44 in any stageS1-S22 of the compressor section 14. Accordingly, the airfoil shapedefined by each of TABLES I and II should not be limited to anyparticular stage of the compressor section 14 unless specificallyrecited in the claims.

FIG. 3 illustrates a perspective view of a stator vane 50, which may beincorporated in any stage (e.g., S1 through S22) of the compressorsection 14, in accordance with embodiments of the present disclosure.

As shown, the stator vane 50 includes an airfoil 100 defining an airfoilshape 150. The airfoil 100 includes a pressure-side surface or profile102 and an opposing suction-side surface or profile 104. Thepressure-side surface 102 and the suction-side surface 104 meet orintersect at a leading edge 106 and a trailing edge 108 of the airfoil100. A chord line 110 extends between the leading edge 106 and thetrailing edge 108 such that pressure and suction-side surfaces 102, 104can be said to extend in chord or chordwise between the leading edge 106and the trailing edge 108. The leading and trailing edges, 106 and 108respectively, may be described as the dividing or intersecting linesbetween the suction-side surface 104 and the pressure-side surface 102.In other words, the suction-side surface 104 and the pressure-sidesurface 102 couple together with one another along the leading edge 106and the trailing edge 108, thereby defining an airfoil shapedcross-section that gradually changes lengthwise (or “span-wise”) alongthe airfoil 100.

In operation, the stator vanes 50 may be stationary components that donot move in the circumferential direction C. For example, the statorvanes 50 may be coupled to, and extend radially inward from, thecompressor casing 48. Each set (or stage) of stator vanes 50 within thecompressor section 14 may be disposed axially between two sets (orstages) of rotor blades 44, which rotate in the circumferentialdirection C. For example, the rotor blades 44 rotate about theturbomachine axial centerline 23 exerting a torque on a working fluid,such as air 15, thus increasing energy levels of the fluid as theworking fluid traverses the various stages S1 through S22 of themulti-stage axial compressor section 14 on its way to the combustorsection 16. The stator vanes 50 may be adjacent (e.g., upstream and/ordownstream) to the one or more sets of the rotor blades 44. The statorvanes 50 slow the working fluid during rotation of the rotor blades 44,converting a circumferential component of movement of the working fluidflow into pressure. Accordingly, continuous rotation of the rotor blade44 creates a continuous flow of compressed working fluid, suitable forcombustion via the combustor section 16.

As shown in FIG. 3 , the airfoil 100 includes a root or first end 112,which intersects with and extends radially inwardly from a base orplatform 114 of the stator vane 50. The airfoil 100 terminates radiallyat a second end or radial tip 116 of the airfoil 100. In someembodiments (not shown), the stator vane 50 may include a tip shroud ortip platform extending from the radial tip 116 generally parallel to thebase 114. The pressure-side and suction-side surfaces 102, 104 can besaid to extend in span or in a span-wise direction 118 between the root112 and/or the platform 114 and the radial tip 116 of the airfoil 100.In other words, each stator vane 50 includes an airfoil 100 havingopposing pressure-side and suction-side surfaces 102, 104 that extend inchord or chordwise 110 between opposing leading and trailing edges 106,108 and that extend in span or span-wise 118 between the root 112 andthe radial tip 116 of the airfoil 100.

In particular configurations, the airfoil 100 may include a fillet 72formed between the platform 114 and the airfoil 100 proximate to theroot 112. The fillet 72 can include a weld or braze fillet, which can beformed via conventional MIG welding, TIG welding, brazing, etc., and caninclude a profile that can reduce fluid dynamic losses as a result ofthe presence of fillet 72. In particular embodiments, the platform 114,the airfoil 100 and the fillet 72 can be formed as a single component,such as by casting and/or machining and/or additive manufacturing (suchas 3D printing) and/or any other suitable technique now known or laterdiscovered and/or developed.

In various implementations, the stator vane 50 may include a mountingportion 74 (such as a dovetail joint), which is formed to connect and/orto secure the stator vane 50 to the compressor casing 48. For example,the mounting portion 74 may include a T-shaped structure, a hook, one ormore lateral protrusions, one or more lateral slots, or any combinationthereof. The mounting portion 74 (e.g., dovetail joint) may beconfigured to mount into the compressor casing 48 in an axial directionA, a radial direction R, and/or a circumferential direction C (e.g.,into an axial slot or opening, a radial slot or opening, and/or acircumferential slot or opening).

An important term in this disclosure is “profile”. The profile is therange of the variation between measured points on an airfoil surface andthe ideal position listed in each of TABLES I and II. The actual profileon a manufactured compressor stator vane will be different than those inTABLES I and II, and the design is robust to this variation meaning thatmechanical and aerodynamic function are not impaired. As noted above,a + or −5% profile tolerance is used herein. The X, Y, and Z values areall non-dimensionalized relative to a scaling factor.

The airfoil 100 of the stator vane 50 has a nominal profile at anycross-section taken between the platform 114 or the root 112 and theradial tip 116, e.g., such as the cross section shown in FIG. 4 . A“nominal profile” is the range of variation between measured points onan airfoil surface and the ideal position listed in TABLES I and II. Theactual profile on a manufactured compressor blade may be different fromthose in TABLES I and II (e.g., due to manufacturing tolerances), andthe design is robust to this variation, meaning that mechanical andaerodynamic function are not impaired.

The Cartesian coordinate values of X, Y, and Z provided in each ofTABLES I and II are dimensionless values scalable by a scaling factor,as measured in any given unit of distance (e.g., inches). For example,the X, Y, and Z values in each of TABLES I and II are set forth innon-dimensionalized units, and thus a variety of units of dimensions maybe used when the values are appropriately scaled by a scaling factor. Asone example only, the Cartesian coordinate values of X, Y, and Z may beconvertible to dimensional distances by multiplying the X, Y, and Zvalues by a scaling factor. The scaling factor may be substantiallyequal to 1, greater than 1, or less than 1. The scaling factor, used toconvert the non-dimensional values to dimensional distances, may be afraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25,etc.), integer (e.g., 1, 2, 10, 100, etc.) or a mixed number (e.g., 1½,10¼, etc.). The scaling factor may be a dimensional distance in anysuitable format (e.g., inches, feet, millimeters, centimeters, etc.). Invarious embodiments, the scaling factor may be between about 0.01 inchesand about 10 inches, or such as between about 0.02 inches and about 5inches, or such as between about 0.04 inches and about 2.5 inches, orsuch as between about 0.06 inches and about 1.5 inches.

In various embodiments, the X, Y, and Z values in each of TABLES I andII may be scaled as a function of the same scaling factor (e.g.,constant or number) to provide a scaled-up or a scaled-down airfoil. Insome embodiments, the scaling factor may be different for each of TABLESI and II, such that each of the TABLES I and II has a unique scalingfactor. In this way, each of TABLES I and II defines the relationshipsbetween the respective X, Y, and Z coordinate values without specifyingthe units of measure (e.g., dimensional units) for the various airfoil100 embodiments. Accordingly, while different scaling factors may beapplied to the respective X, Y, and Z coordinate values of each ofTABLES I and II to define different embodiments of the airfoil 100, eachembodiment of the airfoil 100 regardless of the particular scalingfactor is considered to be defined by the respective X, Y, and Zcoordinate values TABLES I and II. For example, the X, Y, and Zcoordinate values of TABLES I and II may each define an embodiment ofthe airfoil 100 formed with a 1:1 inch scaling factor, or formed with a1:2 inch scaling factor, or formed with a 1:1 cm scaling factor. It maybe appreciated that any scaling factor may be used with the X, Y, and Zcoordinate values of any of TABLES I and II, according to the designconsiderations of a particular embodiment.

A gas turbine hot gas path requires airfoils that meet systemrequirements of aerodynamic and mechanical blade loading and efficiency.To define the airfoil shape of each compressor stator vane airfoil,there is a unique set or loci of points in space that meet the stagerequirements and that can be manufactured. This unique loci of pointsmeet the requirements for stage efficiency and are arrived at byiteration between aerodynamic and mechanical loadings enabling theturbine to run in an efficient, safe and smooth manner. These points areunique and specific to the system.

The loci that define the compressor stator vane airfoil shape include aset of points with X, Y, and Z dimensions relative to a reference origincoordinate system. The Cartesian coordinate system of X, Y, and Z valuesgiven in each of TABLES I and II below defines the airfoil shapes (whichinclude the various airfoil profile sections) of an airfoil belonging toone or more compressor stator vanes at various locations along itsheight (or along the span-wise direction 118).

Each of TABLES I and II list data for an uncoated airfoil at cold orroom temperature. As used herein, the phrase “substantially inaccordance with Cartesian coordinate values of X, Y, and Z set forth inone of TABLE I (or II)” refers to the envelope/tolerance for thecoordinates is about +/−5% in a direction normal to any airfoil surfacelocation and/or about +/−5% of the chord 110 in a direction nominal toany airfoil surface location. In other words, the airfoil layout, asembodied by the disclosure, is robust to this range of variation withoutimpairment of mechanical and aerodynamic functions.

A point data origin 76 is defined at the base 114 of the airfoil 100.For example, the point data origin 76 may be defined at the root 112 ofthe airfoil 100. For example, in some embodiments, the point data origin76 may be defined at the root 112 of the airfoil 100 at the intersectionof a stacking axis (e.g., a radially extending axis) and the compressedair flowpath (e.g., a flowpath of air along the surface of the airfoil).The point data origin 76 corresponds to the non-dimensional Z valueequal to 0.

As described above, the Cartesian coordinate system has orthogonallyrelated (e.g., mutually orthogonal) X, Y, and Z axes, and the X axislies parallel to an axial centerline 23 of the shaft 22, i.e., therotary axis, and a positive X coordinate value is axial toward an aft,i.e., exhaust, end of the gas turbine 10. The positive Y coordinatevalue extends in the direction from the pressure-side surface 102towards the suction-side surface 104, and the positive Z coordinatevalue is radially outwardly from the base 114 toward the radial tip 116(e.g., opposite the radial direction of the gas turbine 10). All thevalues in each of TABLES I and II are given at room temperature and donot include the fillet 72 or coatings (not shown).

By defining X and Y coordinate values at selected locations in a Zdirection normal to the X, Y plane, an airfoil profile section 160 ofthe airfoil 100 of the stator vane 50 may be defined at each specified Zdistance along the length of the airfoil 100. By connecting the X and Yvalues with smooth continuing arcs, each airfoil profile section of theairfoil 100 at each distance Z may be fixed. The complete airfoil shape150 may be determined by smoothly connecting the adjacent profilesections to one another.

The values of TABLES I and II are generated and shown to three decimalplaces for determining the airfoil shape 150 of the airfoil 100. As thestator vane 50 heats up during operation of the gas turbine 10, surfacestress and temperature will cause a change in the X, Y, and Z values.Accordingly, the values for the various airfoil profile sections givenin TABLES I and II define the “nominal” airfoil profile, that is, theprofile of an uncoated airfoil at ambient, non-operating or non-hotconditions (e.g., room temperature).

There are typical manufacturing tolerances as well as coatings whichmust be accounted for in the actual profile of the airfoil 100. Eachcross-section is joined smoothly with the other cross-sections to formthe complete airfoil shape. It will therefore be appreciated that +/−typical manufacturing tolerances, i.e., +/− values, including anycoating thicknesses, are additive to the X and Y values given in each ofTABLES I and II below. Accordingly, a distance of +/−5% in a directionnormal to any surface location along the airfoil profile defines anairfoil profile envelope for this particular stator vane 50 airfoildesign, i.e., a range of variation between measured points on the actualairfoil surface at nominal cold or room temperature and the idealposition of those points as given in each of TABLES I and II below atthe same temperature. The data provided in each of TABLES I and II isscalable (i.e., by a uniform geometric scaling factor), and the geometrypertains to all aerodynamic scales, at, above and/or below 3000 RPM. Thedesign of the airfoil 100 for stator vane 50 is robust to this range ofvariation without impairment of mechanical and aerodynamic functions.

The airfoil 100 may include various airfoil profile sections along thespan-wise direction 118. Each of the airfoil profile sections may be“stacked” on top of one another other along the Z direction, such thatwhen connected with smooth continuous arcs, the complete airfoil shape150 may be ascertained. For example, each airfoil profile sectioncorresponds to Cartesian coordinate values of X, Y, and Z for a commonCartesian coordinate value of Z in each of TABLES I and II. Furthermore,adjacent airfoil profile sections correspond to the Cartesian coordinatevalues of X, Y, and Z for adjacent Cartesian coordinate values of Z ineach of TABLES I and II.

For example, FIG. 4 illustrates an airfoil profile section 160 of anairfoil 100 from along the line 4-4 shown in FIG. 3 , which may berepresentative of an airfoil profile section of the airfoil 100 at anyspan-wise location, in accordance with embodiments of the presentdisclosure. As should be appreciated, the airfoil shape 150 of theairfoil 100 may change or vary at each span-wise location (or at eachrespective Z value). In this way, a distinct airfoil profile section 160may be defined at each position along the span-wise direction 118 (or ateach Z value) of the airfoil 100. The airfoil profile sections 160 ateach span-wise location (e.g., at each Z value) of the airfoil 100 areconnected together with smooth continuous lines, thereby defining thecomplete airfoil shape 150 of the airfoil 100.

A Cartesian coordinate system of X, Y, and Z values given in each ofTABLES I and II below defines respective suction side surfaces orprofiles 104 and pressure side surfaces or profiles 102 of therespective airfoils 100 at various locations along the span-wisedirection 118 of the respective airfoils 100. For example, in each ofTABLES I and II, points 113 through 168 define the respective suctionside surface 104 and pressure side surface 102 of a respective airfoiltaken along the Z value coinciding with line 4-4 shown in FIG. 3 .

By defining X and Y coordinate values at selected locations in a Zdirection normal to the X-Y plane, an airfoil profile section 160 of theairfoil 100 may be obtained at each of the selected Z value location(e.g., by connecting each X and Y coordinate value at a given Z value toadjacent X and Y coordinate values of that same Z value with smoothcontinuing arcs). At each Z value or location, the suction side profile104 may joined to the pressure-side profile or surface 102, as shown inFIG. 4 , to define the airfoil profile section 160. The airfoil shape150 of the airfoil 100 may be determined by smoothly connecting theadjacent (e.g., “stacked”) airfoil profile sections 160 to one anotherwith smooth continuous arcs.

The values in each of TABLES I and II below are computer-generated andshown to three decimal places. In certain embodiments, any values havingless than three decimal places may be shown with trailing zeroes toobtain three decimal places. Furthermore, in some embodiments and inview of manufacturing constraints, actual values useful for forming theairfoil 100 may be considered valid to fewer than three decimal placesfor determining the airfoil shape 150 of the airfoil 100.

As will be appreciated, there are typical manufacturing tolerances whichmay be accounted for in the airfoil shape 150. Accordingly, the X, Y,and Z values given in each of TABLES I and II are for the airfoil shape150 of a nominal airfoil. It will therefore be appreciated that plus orminus typical manufacturing tolerances are applicable to these X, Y, andZ values and that an airfoil 100 having a profile substantially inaccordance with those values includes such tolerances.

As noted previously, the airfoil 100 may also be coated for protectionagainst corrosion, erosion, wear, and oxidation after the airfoil 100 ismanufactured, according to the values in any of TABLES I and II andwithin the tolerances explained above. For example, the coating regionmay include one or more corrosion resistant layers, erosion resistantlayers, wear resistant layers, oxidation resistant or anti-oxidationlayers, or any combination thereof. For example, in embodiments wherethe airfoil is measured in inches, an anti-corrosion coating may beprovided with an average thickness of 0.008 inches (0.20 mm), or between0.001 and 0.1 inches (between 0.025 and 2.5 mm), or between 0.0001 and 1inches or more (between 0.0025 and 12.7 mm or more). For example, incertain embodiments, the coating may increase X and Y values of asuction side or a pressure side in any of TABLES I and II by no greaterthan approximately 3.5 mm along a first suction portion, a firstpressure portion, or both. It is to be noted that additionalanti-oxidation coatings may be provided, such as overcoats. The valuesprovided in each of TABLES I and II exclude a coated region or coatingsof the airfoil 100. In other words, these values correspond to the baresurface of the airfoil 100. The coated region may include one or morecoating layers, surface treatments, or a combination thereof, over thebare surface of the airfoil 100.

TABLES I and II below each contain Cartesian coordinate data of anairfoil shape 150 of an airfoil 100, which may be incorporated into thecompressor section 14 of the gas turbine 10.

In exemplary embodiments, TABLE I below contains Cartesian coordinatedata of an airfoil shape 150 of an airfoil 100 of a stator vane 50,which is disposed in the mid stage 62 of the compressor section 14.Specifically, TABLE I below contains Cartesian coordinate data of anairfoil shape 150 of an airfoil 100 of a stator vane 50, which isdisposed in the seventeenth stage S17 of the compressor section 14.

TABLE I PRESSURE SIDE SUCTION SIDE N X Y Z X Y Z 1 −0.530 −0.665 −0.0060.743 0.672 −0.006 2 −0.529 −0.665 −0.006 0.742 0.673 −0.006 3 −0.528−0.665 −0.006 0.742 0.674 −0.006 4 −0.527 −0.665 −0.006 0.740 0.676−0.006 5 −0.524 −0.664 −0.006 0.737 0.678 −0.006 6 −0.520 −0.661 −0.0060.730 0.679 −0.006 7 −0.515 −0.655 −0.006 0.722 0.676 −0.006 8 −0.508−0.646 −0.006 0.711 0.672 −0.006 9 −0.502 −0.632 −0.006 0.696 0.666−0.006 10 −0.494 −0.615 −0.006 0.677 0.659 −0.006 11 −0.485 −0.592−0.006 0.653 0.649 −0.006 12 −0.474 −0.566 −0.006 0.625 0.638 −0.006 13−0.462 −0.538 −0.006 0.595 0.626 −0.006 14 −0.448 −0.507 −0.006 0.5630.614 −0.006 15 −0.432 −0.473 −0.006 0.528 0.600 −0.006 16 −0.413 −0.436−0.006 0.487 0.583 −0.006 17 −0.393 −0.398 −0.006 0.445 0.565 −0.006 18−0.371 −0.358 −0.006 0.401 0.546 −0.006 19 −0.347 −0.317 −0.006 0.3550.526 −0.006 20 −0.321 −0.276 −0.006 0.308 0.504 −0.006 21 −0.293 −0.234−0.006 0.259 0.480 −0.006 22 −0.262 −0.191 −0.006 0.209 0.455 −0.006 23−0.229 −0.147 −0.006 0.158 0.427 −0.006 24 −0.193 −0.103 −0.006 0.1060.397 −0.006 25 −0.156 −0.060 −0.006 0.055 0.365 −0.006 26 −0.119 −0.018−0.006 0.006 0.331 −0.006 27 −0.080 0.024 −0.006 −0.043 0.296 −0.006 28−0.041 0.065 −0.006 −0.090 0.259 −0.006 29 −0.002 0.105 −0.006 −0.1350.219 −0.006 30 0.038 0.145 −0.006 −0.178 0.177 −0.006 31 0.079 0.185−0.006 −0.219 0.133 −0.006 32 0.120 0.223 −0.006 −0.258 0.087 −0.006 330.162 0.261 −0.006 −0.293 0.039 −0.006 34 0.205 0.298 −0.006 −0.327−0.011 −0.006 35 0.249 0.334 −0.006 −0.358 −0.063 −0.006 36 0.292 0.367−0.006 −0.385 −0.114 −0.006 37 0.335 0.399 −0.006 −0.409 −0.164 −0.00638 0.376 0.429 −0.006 −0.431 −0.214 −0.006 39 0.416 0.457 −0.006 −0.450−0.262 −0.006 40 0.456 0.483 −0.006 −0.467 −0.309 −0.006 41 0.493 0.508−0.006 −0.482 −0.355 −0.006 42 0.530 0.531 −0.006 −0.495 −0.399 −0.00643 0.565 0.553 −0.006 −0.507 −0.442 −0.006 44 0.596 0.572 −0.006 −0.517−0.480 −0.006 45 0.623 0.589 −0.006 −0.525 −0.516 −0.006 46 0.649 0.604−0.006 −0.532 −0.547 −0.006 47 0.673 0.619 −0.006 −0.538 −0.576 −0.00648 0.694 0.631 −0.006 −0.542 −0.602 −0.006 49 0.711 0.641 −0.006 −0.543−0.622 −0.006 50 0.723 0.649 −0.006 −0.543 −0.638 −0.006 51 0.733 0.655−0.006 −0.541 −0.650 −0.006 52 0.740 0.659 −0.006 −0.538 −0.658 −0.00653 0.743 0.665 −0.006 −0.535 −0.662 −0.006 54 0.744 0.669 −0.006 −0.532−0.664 −0.006 55 0.743 0.671 −0.006 −0.531 −0.665 −0.006 56 0.743 0.672−0.006 −0.530 −0.665 −0.006 57 −0.534 −0.632 0.057 0.737 0.644 0.057 58−0.534 −0.632 0.057 0.737 0.645 0.057 59 −0.533 −0.632 0.057 0.737 0.6460.057 60 −0.532 −0.632 0.057 0.735 0.647 0.057 61 −0.529 −0.632 0.0570.732 0.650 0.057 62 −0.525 −0.629 0.057 0.725 0.651 0.057 63 −0.519−0.623 0.057 0.717 0.648 0.057 64 −0.513 −0.614 0.057 0.706 0.644 0.05765 −0.505 −0.602 0.057 0.692 0.638 0.057 66 −0.497 −0.585 0.057 0.6730.631 0.057 67 −0.487 −0.564 0.057 0.650 0.622 0.057 68 −0.475 −0.5390.057 0.623 0.612 0.057 69 −0.462 −0.513 0.057 0.594 0.600 0.057 70−0.447 −0.483 0.057 0.563 0.588 0.057 71 −0.429 −0.451 0.057 0.529 0.5750.057 72 −0.409 −0.416 0.057 0.489 0.559 0.057 73 −0.387 −0.380 0.0570.448 0.541 0.057 74 −0.364 −0.343 0.057 0.405 0.523 0.057 75 −0.338−0.304 0.057 0.360 0.503 0.057 76 −0.311 −0.265 0.057 0.314 0.482 0.05777 −0.281 −0.226 0.057 0.267 0.460 0.057 78 −0.250 −0.185 0.057 0.2180.435 0.057 79 −0.216 −0.144 0.057 0.168 0.409 0.057 80 −0.180 −0.1020.057 0.118 0.380 0.057 81 −0.144 −0.061 0.057 0.068 0.350 0.057 82−0.106 −0.021 0.057 0.019 0.318 0.057 83 −0.068 0.019 0.057 −0.029 0.2850.057 84 −0.030 0.059 0.057 −0.076 0.249 0.057 85 0.009 0.097 0.057−0.120 0.212 0.057 86 0.049 0.136 0.057 −0.163 0.173 0.057 87 0.0890.174 0.057 −0.204 0.131 0.057 88 0.130 0.211 0.057 −0.243 0.088 0.05789 0.171 0.247 0.057 −0.280 0.042 0.057 90 0.213 0.282 0.057 −0.314−0.005 0.057 91 0.256 0.316 0.057 −0.346 −0.054 0.057 92 0.299 0.3490.057 −0.374 −0.103 0.057 93 0.340 0.379 0.057 −0.400 −0.151 0.057 940.380 0.408 0.057 −0.423 −0.198 0.057 95 0.420 0.435 0.057 −0.444 −0.2440.057 96 0.458 0.461 0.057 −0.462 −0.289 0.057 97 0.495 0.485 0.057−0.478 −0.333 0.057 98 0.530 0.507 0.057 −0.493 −0.375 0.057 99 0.5650.528 0.057 −0.506 −0.416 0.057 100 0.594 0.547 0.057 −0.517 −0.4530.057 101 0.621 0.563 0.057 −0.526 −0.487 0.057 102 0.646 0.578 0.057−0.533 −0.517 0.057 103 0.670 0.592 0.057 −0.540 −0.546 0.057 104 0.6900.604 0.057 −0.544 −0.571 0.057 105 0.706 0.614 0.057 −0.547 −0.5900.057 106 0.719 0.621 0.057 −0.547 −0.605 0.057 107 0.728 0.627 0.057−0.545 −0.617 0.057 108 0.735 0.631 0.057 −0.542 −0.625 0.057 109 0.7380.637 0.057 −0.539 −0.629 0.057 110 0.738 0.641 0.057 −0.537 −0.6310.057 111 0.738 0.643 0.057 −0.535 −0.632 0.057 112 0.738 0.644 0.057−0.535 −0.632 0.057 113 −0.541 −0.575 0.172 0.728 0.593 0.172 114 −0.541−0.575 0.172 0.728 0.594 0.172 115 −0.540 −0.575 0.172 0.727 0.595 0.172116 −0.539 −0.575 0.172 0.726 0.596 0.172 117 −0.536 −0.575 0.172 0.7230.599 0.172 118 −0.532 −0.573 0.172 0.717 0.600 0.172 119 −0.526 −0.5680.172 0.709 0.597 0.172 120 −0.519 −0.560 0.172 0.699 0.594 0.172 121−0.511 −0.549 0.172 0.685 0.588 0.172 122 −0.501 −0.534 0.172 0.6680.582 0.172 123 −0.490 −0.514 0.172 0.645 0.573 0.172 124 −0.476 −0.4920.172 0.619 0.564 0.172 125 −0.461 −0.469 0.172 0.592 0.553 0.172 126−0.443 −0.443 0.172 0.562 0.542 0.172 127 −0.423 −0.414 0.172 0.5300.529 0.172 128 −0.401 −0.383 0.172 0.492 0.514 0.172 129 −0.377 −0.3500.172 0.453 0.498 0.172 130 −0.351 −0.317 0.172 0.412 0.481 0.172 131−0.324 −0.283 0.172 0.370 0.463 0.172 132 −0.294 −0.248 0.172 0.3260.443 0.172 133 −0.264 −0.213 0.172 0.281 0.422 0.172 134 −0.231 −0.1760.172 0.234 0.399 0.172 135 −0.196 −0.139 0.172 0.187 0.375 0.172 136−0.160 −0.101 0.172 0.138 0.349 0.172 137 −0.124 −0.064 0.172 0.0900.321 0.172 138 −0.086 −0.027 0.172 0.043 0.292 0.172 139 −0.049 0.0100.172 −0.004 0.262 0.172 140 −0.011 0.046 0.172 −0.049 0.230 0.172 1410.027 0.082 0.172 −0.093 0.197 0.172 142 0.066 0.117 0.172 −0.136 0.1610.172 143 0.105 0.152 0.172 −0.177 0.124 0.172 144 0.145 0.186 0.172−0.217 0.086 0.172 145 0.185 0.220 0.172 −0.254 0.045 0.172 146 0.2260.253 0.172 −0.290 0.003 0.172 147 0.268 0.285 0.172 −0.324 −0.041 0.172148 0.309 0.315 0.172 −0.355 −0.085 0.172 149 0.348 0.344 0.172 −0.382−0.128 0.172 150 0.387 0.370 0.172 −0.408 −0.171 0.172 151 0.425 0.3960.172 −0.431 −0.213 0.172 152 0.461 0.420 0.172 −0.451 −0.255 0.172 1530.497 0.442 0.172 −0.470 −0.295 0.172 154 0.531 0.464 0.172 −0.486−0.334 0.172 155 0.564 0.484 0.172 −0.501 −0.372 0.172 156 0.592 0.5010.172 −0.514 −0.406 0.172 157 0.617 0.516 0.172 −0.525 −0.438 0.172 1580.642 0.531 0.172 −0.534 −0.466 0.172 159 0.664 0.544 0.172 −0.542−0.492 0.172 160 0.684 0.555 0.172 −0.548 −0.516 0.172 161 0.699 0.5640.172 −0.551 −0.534 0.172 162 0.711 0.571 0.172 −0.551 −0.549 0.172 1630.720 0.576 0.172 −0.550 −0.560 0.172 164 0.726 0.581 0.172 −0.548−0.568 0.172 165 0.729 0.586 0.172 −0.546 −0.571 0.172 166 0.729 0.5900.172 −0.543 −0.573 0.172 167 0.729 0.592 0.172 −0.542 −0.574 0.172 1680.728 0.593 0.172 −0.542 −0.575 0.172 169 −0.550 −0.502 0.337 0.7160.525 0.337 170 −0.550 −0.502 0.337 0.716 0.526 0.337 171 −0.549 −0.5020.337 0.715 0.527 0.337 172 −0.548 −0.502 0.337 0.714 0.528 0.337 173−0.545 −0.502 0.337 0.712 0.531 0.337 174 −0.541 −0.501 0.337 0.7060.532 0.337 175 −0.535 −0.498 0.337 0.698 0.530 0.337 176 −0.527 −0.4920.337 0.689 0.527 0.337 177 −0.518 −0.482 0.337 0.676 0.522 0.337 178−0.507 −0.470 0.337 0.659 0.516 0.337 179 −0.493 −0.454 0.337 0.6380.508 0.337 180 −0.477 −0.435 0.337 0.614 0.499 0.337 181 −0.460 −0.4150.337 0.588 0.490 0.337 182 −0.440 −0.393 0.337 0.561 0.479 0.337 183−0.418 −0.369 0.337 0.530 0.468 0.337 184 −0.393 −0.342 0.337 0.4950.454 0.337 185 −0.367 −0.315 0.337 0.458 0.439 0.337 186 −0.339 −0.2870.337 0.420 0.424 0.337 187 −0.310 −0.258 0.337 0.380 0.407 0.337 188−0.280 −0.228 0.337 0.339 0.389 0.337 189 −0.248 −0.197 0.337 0.2970.370 0.337 190 −0.214 −0.166 0.337 0.253 0.350 0.337 191 −0.179 −0.1330.337 0.208 0.328 0.337 192 −0.143 −0.100 0.337 0.162 0.305 0.337 193−0.106 −0.067 0.337 0.116 0.281 0.337 194 −0.069 −0.034 0.337 0.0710.256 0.337 195 −0.032 −0.002 0.337 0.027 0.229 0.337 196 0.006 0.0310.337 −0.017 0.202 0.337 197 0.043 0.063 0.337 −0.060 0.173 0.337 1980.081 0.094 0.337 −0.102 0.143 0.337 199 0.120 0.125 0.337 −0.143 0.1120.337 200 0.159 0.156 0.337 −0.183 0.079 0.337 201 0.198 0.185 0.337−0.222 0.045 0.337 202 0.237 0.215 0.337 −0.259 0.009 0.337 203 0.2770.244 0.337 −0.295 −0.029 0.337 204 0.317 0.271 0.337 −0.328 −0.0660.337 205 0.355 0.297 0.337 −0.358 −0.104 0.337 206 0.392 0.321 0.337−0.386 −0.141 0.337 207 0.428 0.345 0.337 −0.412 −0.177 0.337 208 0.4630.366 0.337 −0.435 −0.214 0.337 209 0.496 0.387 0.337 −0.456 −0.2490.337 210 0.529 0.406 0.337 −0.476 −0.283 0.337 211 0.560 0.425 0.337−0.494 −0.317 0.337 212 0.587 0.441 0.337 −0.509 −0.348 0.337 213 0.6110.454 0.337 −0.522 −0.376 0.337 214 0.634 0.468 0.337 −0.533 −0.4010.337 215 0.656 0.480 0.337 −0.543 −0.425 0.337 216 0.674 0.490 0.337−0.551 −0.446 0.337 217 0.689 0.498 0.337 −0.555 −0.463 0.337 218 0.7000.505 0.337 −0.557 −0.476 0.337 219 0.709 0.509 0.337 −0.557 −0.4870.337 220 0.715 0.514 0.337 −0.556 −0.494 0.337 221 0.717 0.519 0.337−0.554 −0.498 0.337 222 0.717 0.522 0.337 −0.552 −0.500 0.337 223 0.7160.524 0.337 −0.551 −0.501 0.337 224 0.716 0.525 0.337 −0.551 −0.5020.337 225 −0.552 −0.458 0.463 0.707 0.485 0.463 226 −0.552 −0.459 0.4630.707 0.486 0.463 227 −0.551 −0.459 0.463 0.707 0.487 0.463 228 −0.550−0.459 0.463 0.705 0.488 0.463 229 −0.547 −0.460 0.463 0.703 0.490 0.463230 −0.543 −0.459 0.463 0.697 0.492 0.463 231 −0.537 −0.456 0.463 0.6900.490 0.463 232 −0.529 −0.451 0.463 0.681 0.487 0.463 233 −0.519 −0.4430.463 0.669 0.482 0.463 234 −0.507 −0.432 0.463 0.653 0.477 0.463 235−0.492 −0.418 0.463 0.633 0.469 0.463 236 −0.475 −0.401 0.463 0.6100.461 0.463 237 −0.457 −0.384 0.463 0.585 0.451 0.463 238 −0.436 −0.3640.463 0.559 0.442 0.463 239 −0.413 −0.343 0.463 0.530 0.430 0.463 240−0.387 −0.319 0.463 0.496 0.417 0.463 241 −0.360 −0.295 0.463 0.4610.403 0.463 242 −0.332 −0.270 0.463 0.424 0.389 0.463 243 −0.302 −0.2430.463 0.386 0.373 0.463 244 −0.271 −0.216 0.463 0.346 0.356 0.463 245−0.238 −0.189 0.463 0.306 0.338 0.463 246 −0.205 −0.160 0.463 0.2640.319 0.463 247 −0.169 −0.130 0.463 0.220 0.299 0.463 248 −0.133 −0.1000.463 0.176 0.277 0.463 249 −0.096 −0.069 0.463 0.132 0.255 0.463 250−0.059 −0.039 0.463 0.088 0.231 0.463 251 −0.023 −0.009 0.463 0.0450.207 0.463 252 0.015 0.021 0.463 0.002 0.182 0.463 253 0.052 0.0500.463 −0.040 0.156 0.463 254 0.089 0.079 0.463 −0.081 0.129 0.463 2550.127 0.108 0.463 −0.122 0.101 0.463 256 0.165 0.136 0.463 −0.162 0.0720.463 257 0.204 0.164 0.463 −0.200 0.041 0.463 258 0.243 0.192 0.463−0.238 0.009 0.463 259 0.282 0.219 0.463 −0.274 −0.025 0.463 260 0.3200.245 0.463 −0.308 −0.059 0.463 261 0.357 0.269 0.463 −0.340 −0.0920.463 262 0.393 0.292 0.463 −0.369 −0.126 0.463 263 0.428 0.314 0.463−0.396 −0.159 0.463 264 0.462 0.334 0.463 −0.421 −0.192 0.463 265 0.4950.354 0.463 −0.444 −0.224 0.463 266 0.526 0.372 0.463 −0.465 −0.2560.463 267 0.556 0.390 0.463 −0.485 −0.286 0.463 268 0.582 0.404 0.463−0.501 −0.315 0.463 269 0.606 0.418 0.463 −0.516 −0.340 0.463 270 0.6280.430 0.463 −0.529 −0.364 0.463 271 0.649 0.442 0.463 −0.540 −0.3860.463 272 0.667 0.452 0.463 −0.548 −0.405 0.463 273 0.681 0.459 0.463−0.554 −0.421 0.463 274 0.692 0.465 0.463 −0.557 −0.434 0.463 275 0.7000.470 0.463 −0.557 −0.444 0.463 276 0.706 0.474 0.463 −0.557 −0.4510.463 277 0.708 0.479 0.463 −0.555 −0.455 0.463 278 0.708 0.482 0.463−0.554 −0.457 0.463 279 0.708 0.484 0.463 −0.553 −0.458 0.463 280 0.7070.485 0.463 −0.552 −0.458 0.463 281 −0.549 −0.421 0.669 0.705 0.4410.669 282 −0.549 −0.421 0.669 0.705 0.441 0.669 283 −0.549 −0.421 0.6690.704 0.442 0.669 284 −0.548 −0.422 0.669 0.703 0.444 0.669 285 −0.545−0.422 0.669 0.701 0.446 0.669 286 −0.541 −0.422 0.669 0.696 0.447 0.669287 −0.535 −0.420 0.669 0.689 0.446 0.669 288 −0.527 −0.416 0.669 0.6800.443 0.669 289 −0.516 −0.409 0.669 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−0.390 1.497 556 0.655 0.488 1.497 −0.568 −0.397 1.497 5570.658 0.493 1.497 −0.568 −0.401 1.497 558 0.658 0.496 1.497 −0.566−0.403 1.497 559 0.657 0.497 1.497 −0.566 −0.404 1.497 560 0.657 0.4981.497 −0.565 −0.405 1.497 561 −0.572 −0.413 1.638 0.630 0.527 1.638 562−0.572 −0.413 1.638 0.630 0.528 1.638 563 −0.571 −0.413 1.638 0.6300.529 1.638 564 −0.570 −0.414 1.638 0.628 0.530 1.638 565 −0.568 −0.4141.638 0.626 0.532 1.638 566 −0.564 −0.413 1.638 0.620 0.533 1.638 567−0.558 −0.410 1.638 0.614 0.530 1.638 568 −0.550 −0.405 1.638 0.6050.527 1.638 569 −0.541 −0.397 1.638 0.593 0.522 1.638 570 −0.529 −0.3861.638 0.578 0.516 1.638 571 −0.516 −0.372 1.638 0.559 0.509 1.638 572−0.500 −0.355 1.638 0.538 0.500 1.638 573 −0.483 −0.337 1.638 0.5140.490 1.638 574 −0.464 −0.317 1.638 0.490 0.479 1.638 575 −0.442 −0.2951.638 0.462 0.467 1.638 576 −0.419 −0.271 1.638 0.431 0.453 1.638 577−0.394 −0.246 1.638 0.398 0.438 1.638 578 −0.367 −0.220 1.638 0.3640.421 1.638 579 −0.340 −0.193 1.638 0.328 0.404 1.638 580 −0.311 −0.1651.638 0.292 0.385 1.638 581 −0.281 −0.137 1.638 0.254 0.366 1.638 582−0.249 −0.107 1.638 0.215 0.345 1.638 583 −0.216 −0.077 1.638 0.1750.323 1.638 584 −0.182 −0.046 1.638 0.134 0.299 1.638 585 −0.147 −0.0161.638 0.093 0.275 1.638 586 −0.112 0.014 1.638 0.053 0.250 1.638 587−0.077 0.044 1.638 0.013 0.225 1.638 588 −0.041 0.074 1.638 −0.027 0.1991.638 589 −0.006 0.103 1.638 −0.065 0.171 1.638 590 0.030 0.132 1.638−0.103 0.143 1.638 591 0.066 0.161 1.638 −0.141 0.114 1.638 592 0.1030.189 1.638 −0.177 0.084 1.638 593 0.140 0.217 1.638 −0.213 0.053 1.638594 0.177 0.244 1.638 −0.248 0.021 1.638 595 0.215 0.271 1.638 −0.282−0.011 1.638 596 0.252 0.296 1.638 −0.315 −0.044 1.638 597 0.287 0.3201.638 −0.345 −0.076 1.638 598 0.322 0.343 1.638 −0.374 −0.107 1.638 5990.356 0.364 1.638 −0.401 −0.138 1.638 600 0.389 0.384 1.638 −0.426−0.169 1.638 601 0.421 0.403 1.638 −0.450 −0.198 1.638 602 0.451 0.4211.638 −0.472 −0.227 1.638 603 0.481 0.438 1.638 −0.493 −0.255 1.638 6040.506 0.452 1.638 −0.511 −0.280 1.638 605 0.529 0.465 1.638 −0.527−0.303 1.638 606 0.551 0.477 1.638 −0.541 −0.324 1.638 607 0.571 0.4871.638 −0.554 −0.345 1.638 608 0.589 0.497 1.638 −0.563 −0.363 1.638 6090.603 0.504 1.638 −0.570 −0.377 1.638 610 0.614 0.509 1.638 −0.574−0.389 1.638 611 0.622 0.513 1.638 −0.576 −0.398 1.638 612 0.628 0.5171.638 −0.576 −0.405 1.638 613 0.631 0.521 1.638 −0.575 −0.409 1.638 6140.631 0.524 1.638 −0.574 −0.411 1.638 615 0.631 0.526 1.638 −0.573−0.412 1.638 616 0.630 0.527 1.638 −0.572 −0.413 1.638 617 −0.582 −0.4241.798 0.593 0.573 1.798 618 −0.582 −0.424 1.798 0.593 0.574 1.798 619−0.581 −0.424 1.798 0.593 0.575 1.798 620 −0.580 −0.425 1.798 0.5910.576 1.798 621 −0.578 −0.425 1.798 0.589 0.578 1.798 622 −0.574 −0.4231.798 0.583 0.578 1.798 623 −0.568 −0.420 1.798 0.577 0.576 1.798 624−0.561 −0.414 1.798 0.568 0.572 1.798 625 −0.552 −0.405 1.798 0.5560.568 1.798 626 −0.541 −0.394 1.798 0.541 0.562 1.798 627 −0.528 −0.3781.798 0.521 0.554 1.798 628 −0.513 −0.360 1.798 0.499 0.545 1.798 629−0.498 −0.341 1.798 0.476 0.535 1.798 630 −0.480 −0.319 1.798 0.4510.524 1.798 631 −0.460 −0.295 1.798 0.423 0.512 1.798 632 −0.438 −0.2691.798 0.391 0.497 1.798 633 −0.415 −0.242 1.798 0.358 0.481 1.798 634−0.390 −0.214 1.798 0.323 0.464 1.798 635 −0.364 −0.184 1.798 0.2880.446 1.798 636 −0.337 −0.155 1.798 0.251 0.427 1.798 637 −0.308 −0.1241.798 0.213 0.406 1.798 638 −0.278 −0.092 1.798 0.175 0.383 1.798 639−0.246 −0.060 1.798 0.135 0.360 1.798 640 −0.213 −0.027 1.798 0.0940.334 1.798 641 −0.180 0.006 1.798 0.054 0.308 1.798 642 −0.146 0.0381.798 0.014 0.282 1.798 643 −0.112 0.070 1.798 −0.025 0.254 1.798 644−0.077 0.102 1.798 −0.064 0.226 1.798 645 −0.042 0.133 1.798 −0.1020.196 1.798 646 −0.007 0.164 1.798 −0.139 0.165 1.798 647 0.028 0.1941.798 −0.175 0.134 1.798 648 0.064 0.224 1.798 −0.210 0.101 1.798 6490.100 0.254 1.798 −0.245 0.068 1.798 650 0.137 0.282 1.798 −0.278 0.0341.798 651 0.175 0.311 1.798 −0.311 −0.002 1.798 652 0.211 0.337 1.798−0.342 −0.036 1.798 653 0.247 0.362 1.798 −0.371 −0.070 1.798 654 0.2820.386 1.798 −0.398 −0.104 1.798 655 0.316 0.408 1.798 −0.423 −0.1371.798 656 0.349 0.429 1.798 −0.447 −0.169 1.798 657 0.380 0.449 1.798−0.470 −0.200 1.798 658 0.411 0.467 1.798 −0.491 −0.230 1.798 659 0.4410.484 1.798 −0.510 −0.259 1.798 660 0.467 0.499 1.798 −0.528 −0.2861.798 661 0.490 0.511 1.798 −0.543 −0.311 1.798 662 0.512 0.523 1.798−0.556 −0.332 1.798 663 0.533 0.534 1.798 −0.567 −0.354 1.798 664 0.5510.543 1.798 −0.576 −0.372 1.798 665 0.565 0.550 1.798 −0.582 −0.3871.798 666 0.576 0.556 1.798 −0.585 −0.400 1.798 667 0.584 0.560 1.798−0.586 −0.409 1.798 668 0.591 0.563 1.798 −0.586 −0.416 1.798 669 0.5940.567 1.798 −0.585 −0.420 1.798 670 0.594 0.570 1.798 −0.584 −0.4221.798 671 0.594 0.572 1.798 −0.583 −0.423 1.798 672 0.593 0.573 1.798−0.582 −0.424 1.798 673 −0.593 −0.441 1.929 0.554 0.609 1.929 674 −0.593−0.441 1.929 0.553 0.609 1.929 675 −0.593 −0.441 1.929 0.553 0.610 1.929676 −0.591 −0.441 1.929 0.552 0.611 1.929 677 −0.589 −0.441 1.929 0.5490.613 1.929 678 −0.585 −0.439 1.929 0.544 0.614 1.929 679 −0.579 −0.4351.929 0.537 0.611 1.929 680 −0.572 −0.429 1.929 0.528 0.608 1.929 681−0.564 −0.420 1.929 0.516 0.603 1.929 682 −0.554 −0.407 1.929 0.5000.597 1.929 683 −0.542 −0.390 1.929 0.481 0.590 1.929 684 −0.529 −0.3711.929 0.458 0.581 1.929 685 −0.515 −0.350 1.929 0.434 0.571 1.929 686−0.499 −0.327 1.929 0.409 0.560 1.929 687 −0.480 −0.301 1.929 0.3810.547 1.929 688 −0.460 −0.273 1.929 0.348 0.532 1.929 689 −0.439 −0.2441.929 0.315 0.516 1.929 690 −0.416 −0.213 1.929 0.280 0.499 1.929 691−0.391 −0.182 1.929 0.244 0.480 1.929 692 −0.366 −0.150 1.929 0.2070.460 1.929 693 −0.339 −0.117 1.929 0.169 0.438 1.929 694 −0.310 −0.0841.929 0.130 0.415 1.929 695 −0.280 −0.049 1.929 0.090 0.390 1.929 696−0.249 −0.014 1.929 0.049 0.363 1.929 697 −0.217 0.021 1.929 0.009 0.3361.929 698 −0.184 0.055 1.929 −0.031 0.308 1.929 699 −0.151 0.089 1.929−0.069 0.278 1.929 700 −0.117 0.122 1.929 −0.107 0.247 1.929 701 −0.0830.155 1.929 −0.144 0.216 1.929 702 −0.049 0.187 1.929 −0.180 0.183 1.929703 −0.014 0.219 1.929 −0.215 0.149 1.929 704 0.022 0.251 1.929 −0.2490.114 1.929 705 0.058 0.281 1.929 −0.281 0.078 1.929 706 0.094 0.3111.929 −0.313 0.041 1.929 707 0.131 0.341 1.929 −0.345 0.004 1.929 7080.168 0.368 1.929 −0.374 −0.033 1.929 709 0.204 0.394 1.929 −0.401−0.070 1.929 710 0.238 0.419 1.929 −0.427 −0.105 1.929 711 0.272 0.4421.929 −0.451 −0.140 1.929 712 0.306 0.463 1.929 −0.473 −0.174 1.929 7130.338 0.483 1.929 −0.494 −0.207 1.929 714 0.369 0.502 1.929 −0.513−0.238 1.929 715 0.399 0.519 1.929 −0.531 −0.269 1.929 716 0.425 0.5341.929 −0.547 −0.297 1.929 717 0.448 0.547 1.929 −0.561 −0.323 1.929 7180.471 0.559 1.929 −0.573 −0.346 1.929 719 0.492 0.569 1.929 −0.583−0.368 1.929 720 0.510 0.579 1.929 −0.591 −0.388 1.929 721 0.524 0.5861.929 −0.595 −0.404 1.929 722 0.536 0.591 1.929 −0.598 −0.416 1.929 7230.544 0.595 1.929 −0.599 −0.426 1.929 724 0.550 0.598 1.929 −0.598−0.433 1.929 725 0.554 0.603 1.929 −0.597 −0.437 1.929 726 0.554 0.6061.929 −0.595 −0.439 1.929 727 0.554 0.608 1.929 −0.594 −0.440 1.929 7280.554 0.608 1.929 −0.594 −0.440 1.929 729 −0.604 −0.460 2.025 0.5220.634 2.025 730 −0.604 −0.460 2.025 0.522 0.634 2.025 731 −0.603 −0.4602.025 0.521 0.635 2.025 732 −0.602 −0.460 2.025 0.520 0.636 2.025 733−0.599 −0.460 2.025 0.517 0.638 2.025 734 −0.596 −0.458 2.025 0.5120.638 2.025 735 −0.590 −0.454 2.025 0.505 0.636 2.025 736 −0.583 −0.4472.025 0.495 0.633 2.025 737 −0.576 −0.437 2.025 0.483 0.628 2.025 738−0.567 −0.423 2.025 0.468 0.622 2.025 739 −0.556 −0.406 2.025 0.4480.615 2.025 740 −0.544 −0.385 2.025 0.425 0.606 2.025 741 −0.531 −0.3632.025 0.400 0.596 2.025 742 −0.516 −0.338 2.025 0.374 0.585 2.025 743−0.500 −0.311 2.025 0.346 0.572 2.025 744 −0.481 −0.281 2.025 0.3130.557 2.025 745 −0.461 −0.250 2.025 0.278 0.541 2.025 746 −0.440 −0.2182.025 0.243 0.523 2.025 747 −0.417 −0.185 2.025 0.206 0.504 2.025 748−0.393 −0.151 2.025 0.169 0.484 2.025 749 −0.368 −0.116 2.025 0.1300.461 2.025 750 −0.341 −0.081 2.025 0.091 0.438 2.025 751 −0.312 −0.0442.025 0.050 0.412 2.025 752 −0.282 −0.007 2.025 0.009 0.384 2.025 753−0.251 0.029 2.025 −0.031 0.356 2.025 754 −0.219 0.065 2.025 −0.0710.326 2.025 755 −0.186 0.100 2.025 −0.109 0.295 2.025 756 −0.153 0.1352.025 −0.146 0.262 2.025 757 −0.120 0.169 2.025 −0.182 0.229 2.025 758−0.085 0.203 2.025 −0.217 0.194 2.025 759 −0.051 0.236 2.025 −0.2510.158 2.025 760 −0.015 0.268 2.025 −0.284 0.121 2.025 761 0.021 0.3002.025 −0.316 0.083 2.025 762 0.057 0.331 2.025 −0.347 0.044 2.025 7630.094 0.361 2.025 −0.377 0.004 2.025 764 0.131 0.390 2.025 −0.404 −0.0342.025 765 0.167 0.417 2.025 −0.430 −0.073 2.025 766 0.202 0.442 2.025−0.454 −0.110 2.025 767 0.236 0.465 2.025 −0.477 −0.147 2.025 768 0.2700.487 2.025 −0.497 −0.182 2.025 769 0.302 0.507 2.025 −0.517 −0.2172.025 770 0.334 0.526 2.025 −0.535 −0.250 2.025 771 0.364 0.544 2.025−0.551 −0.282 2.025 772 0.391 0.559 2.025 −0.566 −0.312 2.025 773 0.4150.572 2.025 −0.579 −0.339 2.025 774 0.437 0.583 2.025 −0.590 −0.3632.025 775 0.459 0.594 2.025 −0.598 −0.386 2.025 776 0.477 0.604 2.025−0.605 −0.406 2.025 777 0.492 0.611 2.025 −0.608 −0.422 2.025 778 0.5030.616 2.025 −0.610 −0.435 2.025 779 0.512 0.620 2.025 −0.610 −0.4452.025 780 0.518 0.623 2.025 −0.609 −0.453 2.025 781 0.522 0.627 2.025−0.608 −0.456 2.025 782 0.523 0.630 2.025 −0.606 −0.459 2.025 783 0.5220.632 2.025 −0.605 −0.459 2.025 784 0.522 0.633 2.025 −0.604 −0.4602.025 785 −0.614 −0.482 2.122 0.488 0.656 2.122 786 −0.613 −0.482 2.1220.487 0.657 2.122 787 −0.613 −0.482 2.122 0.487 0.658 2.122 788 −0.611−0.482 2.122 0.486 0.659 2.122 789 −0.609 −0.481 2.122 0.483 0.661 2.122790 −0.605 −0.479 2.122 0.477 0.661 2.122 791 −0.600 −0.474 2.122 0.4700.658 2.122 792 −0.594 −0.467 2.122 0.461 0.655 2.122 793 −0.587 −0.4562.122 0.448 0.651 2.122 794 −0.578 −0.442 2.122 0.432 0.645 2.122 795−0.569 −0.423 2.122 0.412 0.637 2.122 796 −0.558 −0.401 2.122 0.3880.629 2.122 797 −0.547 −0.378 2.122 0.363 0.619 2.122 798 −0.534 −0.3522.122 0.337 0.608 2.122 799 −0.520 −0.323 2.122 0.307 0.595 2.122 800−0.503 −0.291 2.122 0.274 0.581 2.122 801 −0.486 −0.258 2.122 0.2390.564 2.122 802 −0.466 −0.224 2.122 0.202 0.547 2.122 803 −0.446 −0.1892.122 0.165 0.528 2.122 804 −0.424 −0.154 2.122 0.127 0.507 2.122 805−0.400 −0.117 2.122 0.087 0.484 2.122 806 −0.375 −0.079 2.122 0.0470.460 2.122 807 −0.348 −0.041 2.122 0.006 0.434 2.122 808 −0.319 −0.0022.122 −0.035 0.405 2.122 809 −0.289 0.037 2.122 −0.076 0.375 2.122 810−0.258 0.074 2.122 −0.115 0.344 2.122 811 −0.226 0.111 2.122 −0.1530.311 2.122 812 −0.193 0.147 2.122 −0.190 0.276 2.122 813 −0.160 0.1822.122 −0.226 0.241 2.122 814 −0.126 0.217 2.122 −0.260 0.204 2.122 815−0.091 0.251 2.122 −0.293 0.166 2.122 816 −0.056 0.285 2.122 −0.3250.127 2.122 817 −0.020 0.317 2.122 −0.355 0.087 2.122 818 0.017 0.3502.122 −0.385 0.046 2.122 819 0.054 0.381 2.122 −0.413 0.004 2.122 8200.090 0.410 2.122 −0.439 −0.037 2.122 821 0.127 0.438 2.122 −0.463−0.077 2.122 822 0.162 0.463 2.122 −0.485 −0.117 2.122 823 0.197 0.4872.122 −0.506 −0.155 2.122 824 0.231 0.509 2.122 −0.525 −0.193 2.122 8250.264 0.530 2.122 −0.542 −0.229 2.122 826 0.296 0.549 2.122 −0.558−0.264 2.122 827 0.327 0.567 2.122 −0.573 −0.298 2.122 828 0.354 0.5822.122 −0.586 −0.329 2.122 829 0.378 0.594 2.122 −0.597 −0.357 2.122 8300.401 0.606 2.122 −0.606 −0.382 2.122 831 0.423 0.617 2.122 −0.613−0.406 2.122 832 0.442 0.626 2.122 −0.618 −0.427 2.122 833 0.456 0.6332.122 −0.620 −0.444 2.122 834 0.468 0.639 2.122 −0.621 −0.457 2.122 8350.477 0.643 2.122 −0.621 −0.467 2.122 836 0.484 0.646 2.122 −0.619−0.475 2.122 837 0.487 0.650 2.122 −0.617 −0.479 2.122 838 0.488 0.6532.122 −0.616 −0.481 2.122 839 0.488 0.655 2.122 −0.614 −0.481 2.122 8400.488 0.656 2.122 −0.614 −0.482 2.122

In exemplary embodiments, TABLE II below contains Cartesian coordinatedata of an airfoil shape 150 of an airfoil 100 of a stator vane 50,which is disposed in the mid stage 62 of the compressor section 14.Specifically, TABLE II below contains Cartesian coordinate data of anairfoil shape 150 of an airfoil 100 of a stator vane 50, which isdisposed in the eighteenth stage S18 of the compressor section 14.

TABLE II PRESSURE SIDE SUCTION SIDE N X Y Z X Y Z 1 −0.532 −0.788 −0.0050.956 0.811 −0.005 2 −0.531 −0.788 −0.005 0.955 0.811 −0.005 3 −0.530−0.788 −0.005 0.955 0.812 −0.005 4 −0.528 −0.788 −0.005 0.953 0.815−0.005 5 −0.525 −0.787 −0.005 0.949 0.817 −0.005 6 −0.520 −0.784 −0.0050.941 0.818 −0.005 7 −0.514 −0.776 −0.005 0.931 0.815 −0.005 8 −0.506−0.766 −0.005 0.918 0.809 −0.005 9 −0.497 −0.750 −0.005 0.901 0.802−0.005 10 −0.488 −0.730 −0.005 0.879 0.793 −0.005 11 −0.476 −0.703−0.005 0.851 0.781 −0.005 12 −0.463 −0.673 −0.005 0.818 0.767 −0.005 13−0.447 −0.641 −0.005 0.784 0.752 −0.005 14 −0.430 −0.605 −0.005 0.7470.736 −0.005 15 −0.410 −0.565 −0.005 0.706 0.718 −0.005 16 −0.387 −0.522−0.005 0.659 0.697 −0.005 17 −0.362 −0.478 −0.005 0.610 0.674 −0.005 18−0.334 −0.432 −0.005 0.559 0.650 −0.005 19 −0.305 −0.385 −0.005 0.5060.625 −0.005 20 −0.273 −0.336 −0.005 0.451 0.597 −0.005 21 −0.239 −0.287−0.005 0.395 0.567 −0.005 22 −0.202 −0.237 −0.005 0.337 0.536 −0.005 23−0.163 −0.186 −0.005 0.278 0.501 −0.005 24 −0.121 −0.134 −0.005 0.2180.464 −0.005 25 −0.079 −0.082 −0.005 0.159 0.426 −0.005 26 −0.035 −0.032−0.005 0.101 0.385 −0.005 27 0.009 0.018 −0.005 0.045 0.342 −0.005 280.054 0.067 −0.005 −0.010 0.297 −0.005 29 0.100 0.116 −0.005 −0.0620.250 −0.005 30 0.146 0.164 −0.005 −0.113 0.201 −0.005 31 0.193 0.211−0.005 −0.160 0.149 −0.005 32 0.241 0.258 −0.005 −0.206 0.094 −0.005 330.289 0.303 −0.005 −0.248 0.038 −0.005 34 0.339 0.348 −0.005 −0.287−0.021 −0.005 35 0.389 0.392 −0.005 −0.324 −0.081 −0.005 36 0.439 0.433−0.005 −0.357 −0.141 −0.005 37 0.487 0.472 −0.005 −0.386 −0.200 −0.00538 0.535 0.508 −0.005 −0.412 −0.258 −0.005 39 0.581 0.543 −0.005 −0.435−0.315 −0.005 40 0.626 0.576 −0.005 −0.455 −0.370 −0.005 41 0.670 0.606−0.005 −0.474 −0.424 −0.005 42 0.712 0.635 −0.005 −0.490 −0.475 −0.00543 0.752 0.663 −0.005 −0.504 −0.525 −0.005 44 0.787 0.686 −0.005 −0.516−0.571 −0.005 45 0.819 0.707 −0.005 −0.526 −0.612 −0.005 46 0.849 0.727−0.005 −0.534 −0.649 −0.005 47 0.876 0.745 −0.005 −0.541 −0.683 −0.00548 0.901 0.760 −0.005 −0.546 −0.714 −0.005 49 0.919 0.772 −0.005 −0.548−0.737 −0.005 50 0.934 0.782 −0.005 −0.547 −0.756 −0.005 51 0.946 0.789−0.005 −0.545 −0.770 −0.005 52 0.954 0.795 −0.005 −0.541 −0.780 −0.00553 0.957 0.802 −0.005 −0.538 −0.784 −0.005 54 0.957 0.807 −0.005 −0.535−0.787 −0.005 55 0.956 0.809 −0.005 −0.533 −0.787 −0.005 56 0.956 0.810−0.005 −0.532 −0.788 −0.005 57 −0.539 −0.738 0.096 0.951 0.764 0.096 58−0.538 −0.738 0.096 0.950 0.765 0.096 59 −0.538 −0.739 0.096 0.950 0.7660.096 60 −0.536 −0.739 0.096 0.948 0.768 0.096 61 −0.533 −0.738 0.0960.944 0.771 0.096 62 −0.528 −0.735 0.096 0.937 0.772 0.096 63 −0.521−0.729 0.096 0.927 0.769 0.096 64 −0.513 −0.719 0.096 0.915 0.763 0.09665 −0.504 −0.704 0.096 0.898 0.756 0.096 66 −0.493 −0.685 0.096 0.8770.748 0.096 67 −0.480 −0.661 0.096 0.850 0.736 0.096 68 −0.465 −0.6330.096 0.818 0.723 0.096 69 −0.448 −0.603 0.096 0.785 0.709 0.096 70−0.428 −0.569 0.096 0.750 0.694 0.096 71 −0.406 −0.533 0.096 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0.316 0.254 0.208 −0.201 0.042 0.208 146 0.364 0.293 0.208 −0.244−0.008 0.208 147 0.412 0.332 0.208 −0.284 −0.059 0.208 148 0.460 0.3700.208 −0.321 −0.111 0.208 149 0.506 0.405 0.208 −0.354 −0.162 0.208 1500.551 0.438 0.208 −0.385 −0.212 0.208 151 0.594 0.469 0.208 −0.412−0.261 0.208 152 0.637 0.499 0.208 −0.437 −0.310 0.208 153 0.678 0.5270.208 −0.460 −0.357 0.208 154 0.717 0.553 0.208 −0.480 −0.403 0.208 1550.755 0.578 0.208 −0.498 −0.447 0.208 156 0.788 0.600 0.208 −0.514−0.488 0.208 157 0.818 0.619 0.208 −0.527 −0.525 0.208 158 0.846 0.6370.208 −0.538 −0.558 0.208 159 0.872 0.653 0.208 −0.547 −0.589 0.208 1600.895 0.667 0.208 −0.554 −0.617 0.208 161 0.913 0.678 0.208 −0.558−0.638 0.208 162 0.927 0.687 0.208 −0.559 −0.655 0.208 163 0.937 0.6940.208 −0.558 −0.668 0.208 164 0.944 0.700 0.208 −0.556 −0.678 0.208 1650.947 0.706 0.208 −0.553 −0.682 0.208 166 0.947 0.710 0.208 −0.550−0.685 0.208 167 0.947 0.713 0.208 −0.549 −0.686 0.208 168 0.946 0.7140.208 −0.548 −0.686 0.208 169 −0.555 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0.433 0.470 2.055 −0.379−0.144 2.055 655 0.473 0.498 2.055 −0.409 −0.185 2.055 656 0.512 0.5252.055 −0.437 −0.224 2.055 657 0.550 0.550 2.055 −0.464 −0.262 2.055 6580.587 0.573 2.055 −0.488 −0.300 2.055 659 0.622 0.596 2.055 −0.511−0.336 2.055 660 0.653 0.614 2.055 −0.532 −0.369 2.055 661 0.681 0.6312.055 −0.550 −0.399 2.055 662 0.707 0.646 2.055 −0.565 −0.426 2.055 6630.731 0.660 2.055 −0.579 −0.452 2.055 664 0.753 0.672 2.055 −0.589−0.475 2.055 665 0.769 0.681 2.055 −0.595 −0.493 2.055 666 0.783 0.6882.055 −0.599 −0.508 2.055 667 0.793 0.694 2.055 −0.600 −0.520 2.055 6680.800 0.698 2.055 −0.600 −0.528 2.055 669 0.804 0.703 2.055 −0.599−0.533 2.055 670 0.804 0.707 2.055 −0.597 −0.536 2.055 671 0.803 0.7092.055 −0.596 −0.537 2.055 672 0.803 0.710 2.055 −0.595 −0.537 2.055 673−0.607 −0.555 2.218 0.755 0.755 2.218 674 −0.606 −0.555 2.218 0.7550.756 2.218 675 −0.605 −0.555 2.218 0.754 0.757 2.218 676 −0.604 −0.5562.218 0.753 0.759 2.218 677 −0.601 −0.555 2.218 0.749 0.761 2.218 678−0.597 −0.553 2.218 0.743 0.761 2.218 679 −0.589 −0.548 2.218 0.7340.758 2.218 680 −0.581 −0.540 2.218 0.724 0.753 2.218 681 −0.571 −0.5292.218 0.709 0.747 2.218 682 −0.559 −0.514 2.218 0.691 0.739 2.218 683−0.545 −0.493 2.218 0.667 0.729 2.218 684 −0.529 −0.469 2.218 0.6410.717 2.218 685 −0.512 −0.444 2.218 0.612 0.704 2.218 686 −0.493 −0.4152.218 0.582 0.690 2.218 687 −0.471 −0.384 2.218 0.548 0.673 2.218 688−0.447 −0.349 2.218 0.509 0.653 2.218 689 −0.422 −0.313 2.218 0.4690.632 2.218 690 −0.395 −0.276 2.218 0.428 0.610 2.218 691 −0.366 −0.2382.218 0.385 0.585 2.218 692 −0.336 −0.198 2.218 0.341 0.560 2.218 693−0.303 −0.158 2.218 0.296 0.532 2.218 694 −0.270 −0.116 2.218 0.2490.502 2.218 695 −0.234 −0.074 2.218 0.202 0.471 2.218 696 −0.197 −0.0302.218 0.153 0.437 2.218 697 −0.159 0.013 2.218 0.105 0.402 2.218 698−0.120 0.055 2.218 0.058 0.367 2.218 699 −0.081 0.097 2.218 0.012 0.3302.218 700 −0.041 0.139 2.218 −0.033 0.291 2.218 701 0.000 0.180 2.218−0.076 0.252 2.218 702 0.040 0.220 2.218 −0.119 0.211 2.218 703 0.0820.260 2.218 −0.160 0.169 2.218 704 0.124 0.299 2.218 −0.201 0.125 2.218705 0.166 0.338 2.218 −0.240 0.081 2.218 706 0.210 0.375 2.218 −0.2770.036 2.218 707 0.254 0.412 2.218 −0.314 −0.010 2.218 708 0.297 0.4472.218 −0.349 −0.056 2.218 709 0.339 0.480 2.218 −0.381 −0.101 2.218 7100.381 0.511 2.218 −0.411 −0.144 2.218 711 0.421 0.540 2.218 −0.439−0.187 2.218 712 0.460 0.567 2.218 −0.466 −0.229 2.218 713 0.499 0.5932.218 −0.490 −0.269 2.218 714 0.536 0.617 2.218 −0.513 −0.308 2.218 7150.571 0.640 2.218 −0.534 −0.346 2.218 716 0.602 0.659 2.218 −0.553−0.380 2.218 717 0.630 0.675 2.218 −0.570 −0.412 2.218 718 0.657 0.6912.218 −0.584 −0.440 2.218 719 0.682 0.705 2.218 −0.595 −0.467 2.218 7200.704 0.717 2.218 −0.604 −0.491 2.218 721 0.720 0.726 2.218 −0.609−0.510 2.218 722 0.734 0.733 2.218 −0.612 −0.525 2.218 723 0.744 0.7382.218 −0.613 −0.537 2.218 724 0.752 0.743 2.218 −0.612 −0.546 2.218 7250.755 0.748 2.218 −0.610 −0.551 2.218 726 0.756 0.752 2.218 −0.609−0.553 2.218 727 0.755 0.754 2.218 −0.608 −0.554 2.218 728 0.755 0.7552.218 −0.607 −0.555 2.218 729 −0.619 −0.579 2.343 0.713 0.786 2.343 730−0.619 −0.579 2.343 0.713 0.786 2.343 731 −0.618 −0.579 2.343 0.7120.787 2.343 732 −0.616 −0.579 2.343 0.711 0.789 2.343 733 −0.613 −0.5792.343 0.707 0.791 2.343 734 −0.609 −0.576 2.343 0.700 0.791 2.343 735−0.602 −0.571 2.343 0.692 0.788 2.343 736 −0.594 −0.562 2.343 0.6810.783 2.343 737 −0.585 −0.550 2.343 0.666 0.777 2.343 738 −0.574 −0.5342.343 0.648 0.770 2.343 739 −0.561 −0.512 2.343 0.624 0.760 2.343 740−0.547 −0.487 2.343 0.596 0.747 2.343 741 −0.532 −0.460 2.343 0.5670.734 2.343 742 −0.514 −0.430 2.343 0.536 0.720 2.343 743 −0.495 −0.3962.343 0.502 0.704 2.343 744 −0.473 −0.360 2.343 0.463 0.684 2.343 745−0.449 −0.322 2.343 0.422 0.663 2.343 746 −0.424 −0.283 2.343 0.3800.640 2.343 747 −0.397 −0.242 2.343 0.336 0.615 2.343 748 −0.369 −0.2002.343 0.292 0.588 2.343 749 −0.339 −0.158 2.343 0.246 0.560 2.343 750−0.307 −0.114 2.343 0.199 0.530 2.343 751 −0.273 −0.069 2.343 0.1510.497 2.343 752 −0.237 −0.023 2.343 0.102 0.462 2.343 753 −0.201 0.0222.343 0.055 0.426 2.343 754 −0.163 0.067 2.343 0.008 0.388 2.343 755−0.125 0.111 2.343 −0.038 0.349 2.343 756 −0.086 0.154 2.343 −0.0820.308 2.343 757 −0.046 0.196 2.343 −0.125 0.267 2.343 758 −0.006 0.2382.343 −0.166 0.223 2.343 759 0.035 0.280 2.343 −0.206 0.178 2.343 7600.077 0.320 2.343 −0.245 0.133 2.343 761 0.119 0.360 2.343 −0.282 0.0862.343 762 0.162 0.399 2.343 −0.318 0.038 2.343 763 0.206 0.437 2.343−0.353 −0.011 2.343 764 0.249 0.473 2.343 −0.386 −0.059 2.343 765 0.2920.507 2.343 −0.416 −0.106 2.343 766 0.333 0.539 2.343 −0.445 −0.1522.343 767 0.374 0.569 2.343 −0.471 −0.196 2.343 768 0.414 0.597 2.343−0.495 −0.240 2.343 769 0.452 0.623 2.343 −0.518 −0.282 2.343 770 0.4900.647 2.343 −0.539 −0.323 2.343 771 0.526 0.670 2.343 −0.559 −0.3622.343 772 0.557 0.689 2.343 −0.576 −0.398 2.343 773 0.586 0.706 2.343−0.591 −0.431 2.343 774 0.613 0.721 2.343 −0.603 −0.461 2.343 775 0.6380.735 2.343 −0.614 −0.489 2.343 776 0.660 0.747 2.343 −0.621 −0.5142.343 777 0.677 0.756 2.343 −0.625 −0.533 2.343 778 0.691 0.764 2.343−0.627 −0.549 2.343 779 0.701 0.769 2.343 −0.627 −0.561 2.343 780 0.7090.773 2.343 −0.625 −0.570 2.343 781 0.713 0.778 2.343 −0.623 −0.5752.343 782 0.714 0.782 2.343 −0.621 −0.577 2.343 783 0.714 0.784 2.343−0.620 −0.578 2.343 784 0.713 0.785 2.343 −0.619 −0.579 2.343 785 −0.633−0.614 2.491 0.660 0.819 2.491 786 −0.633 −0.615 2.491 0.659 0.820 2.491787 −0.632 −0.615 2.491 0.659 0.821 2.491 788 −0.630 −0.615 2.491 0.6570.823 2.491 789 −0.627 −0.614 2.491 0.654 0.825 2.491 790 −0.623 −0.6112.491 0.647 0.824 2.491 791 −0.617 −0.605 2.491 0.638 0.821 2.491 792−0.610 −0.595 2.491 0.627 0.817 2.491 793 −0.601 −0.582 2.491 0.6120.811 2.491 794 −0.592 −0.565 2.491 0.593 0.803 2.491 795 −0.581 −0.5412.491 0.568 0.793 2.491 796 −0.569 −0.514 2.491 0.540 0.781 2.491 797−0.556 −0.485 2.491 0.510 0.768 2.491 798 −0.542 −0.453 2.491 0.4780.754 2.491 799 −0.525 −0.417 2.491 0.443 0.738 2.491 800 −0.506 −0.3782.491 0.402 0.718 2.491 801 −0.486 −0.337 2.491 0.360 0.697 2.491 802−0.464 −0.295 2.491 0.317 0.674 2.491 803 −0.441 −0.252 2.491 0.2720.649 2.491 804 −0.415 −0.207 2.491 0.226 0.622 2.491 805 −0.388 −0.1612.491 0.180 0.593 2.491 806 −0.359 −0.114 2.491 0.132 0.561 2.491 807−0.327 −0.066 2.491 0.083 0.527 2.491 808 −0.294 −0.018 2.491 0.0340.491 2.491 809 −0.259 0.030 2.491 −0.014 0.452 2.491 810 −0.223 0.0782.491 −0.061 0.412 2.491 811 −0.186 0.124 2.491 −0.106 0.371 2.491 812−0.148 0.169 2.491 −0.149 0.327 2.491 813 −0.109 0.214 2.491 −0.1910.282 2.491 814 −0.068 0.257 2.491 −0.231 0.236 2.491 815 −0.028 0.3002.491 −0.269 0.188 2.491 816 0.014 0.343 2.491 −0.306 0.139 2.491 8170.056 0.384 2.491 −0.342 0.089 2.491 818 0.099 0.425 2.491 −0.376 0.0382.491 819 0.143 0.465 2.491 −0.408 −0.014 2.491 820 0.187 0.502 2.491−0.438 −0.065 2.491 821 0.230 0.537 2.491 −0.466 −0.115 2.491 822 0.2720.570 2.491 −0.491 −0.164 2.491 823 0.313 0.600 2.491 −0.514 −0.2122.491 824 0.353 0.629 2.491 −0.536 −0.259 2.491 825 0.392 0.655 2.491−0.556 −0.304 2.491 826 0.431 0.680 2.491 −0.574 −0.347 2.491 827 0.4680.703 2.491 −0.590 −0.389 2.491 828 0.500 0.722 2.491 −0.605 −0.4272.491 829 0.529 0.739 2.491 −0.617 −0.462 2.491 830 0.556 0.754 2.491−0.627 −0.493 2.491 831 0.582 0.769 2.491 −0.635 −0.522 2.491 832 0.6050.781 2.491 −0.640 −0.548 2.491 833 0.623 0.790 2.491 −0.643 −0.5692.491 834 0.637 0.797 2.491 −0.643 −0.585 2.491 835 0.647 0.803 2.491−0.642 −0.597 2.491 836 0.655 0.807 2.491 −0.640 −0.606 2.491 837 0.6600.812 2.491 −0.638 −0.611 2.491 838 0.661 0.815 2.491 −0.636 −0.6132.491 839 0.660 0.818 2.491 −0.634 −0.614 2.491 840 0.660 0.819 2.491−0.633 −0.614 2.491

It will also be appreciated that the airfoil 100 disclosed in any one ofthe above TABLES I and II may be scaled up or down geometrically for usein other similar turbine designs. Consequently, the coordinate valuesset forth in each of TABLES I and II may be scaled upwardly ordownwardly such that the airfoil profile shape remains unchanged. Ascaled version of the coordinates in each of TABLES I and II would berepresented by X, Y, and Z coordinate values, with the X, Y, and Znon-dimensional coordinate values converted to units of distance (e.g.,inches), multiplied or divided by a constant number.

As shown in FIG. 4 , each airfoil 100 may define a stagger angle α(alpha) measured between the chord line 110 and the axial direction A ofthe gas turbine 10. Specifically, the stagger angle α may be measuredbetween the chord line 110 of an airfoil 100 and the axial centerline 23(or rotary axis) of the gas turbine 10 at the trailing edge 108 of theairfoil 100. The stagger angle α of each airfoil 100 disclosed hereinmay advantageously vary along the span-wise direction 118 (or radialdirection R) according to a respective stagger angle distribution. Thestagger angle distribution may be a collection of stagger angles α for agiven airfoil 100 at each span-wise location (or radial location) alongthe airfoil 100.

In many embodiments, each stage S1-S22 of rotor blades 44 may include aunique stagger angle distribution, such that the collective utilizationof the stages S1-S22 of rotor blades 44 will yield a highly efficientcompressor section 14. For example, each of the airfoils 100 of therotor blades 44 within the first stage S1 may have a first stagger angledistribution, each of the airfoils 100 of the rotor blades 44 within thesecond stage S2 may have a second stagger angle distribution, and so onfor each rotating stage (S1-S22) of the compressor section 14.

Similarly, each stage S1-S22 of stator vanes 50 may include a uniquestagger angle distribution, such that the collective utilization of thestages S1-S22 of stator vanes 50 will yield a highly efficientcompressor section 14. For example, each of the airfoils 100 of thestator vanes 50 within the first stage S1 may have a first stagger angledistribution, each of the airfoils 100 of the stator vanes 50 within thesecond stage S2 may have a second stagger angle distribution, and so onfor each stationary stage (S1-S22) of the compressor section 14.

In accordance with embodiments of the present disclosure, FIGS. 5 and 6each illustrate a graph of a stagger angle distribution, which maybelong to one or more airfoils 100 within a specified stage (e.g.,S1-S22) of the compressor section 14. Each of the graphs may be innon-dimensional units. Specifically, the y-axis illustrates a percentagealong the span-wise direction 118 (e.g., with 0% span representing theinner diameter and 100% span representing the outer diameter). Forexample, with a rotor blade 44, 0% span may represent the base of theairfoil 100, and 100% span may represent the tip of the airfoil 100. Asfor a stator vane 50, 0% span may represent the tip of the airfoil 100,and 100% span may represent the base of the airfoil 100. The x-axisillustrates a ratio between the stagger angle at a specified span-wiselocation and the mid-span stagger angle (e.g., at about 50% span).

Each of the stagger angle distributions is plotted between 15% span and85% span of the respective airfoil 100 to which it belongs (e.g., 0%-15%span and 85%-100% span points are omitted). Each stagger angledistribution, when implemented in an airfoil 100 on a rotor blade 44and/or a stator vane 50 within the compressor section 14, advantageouslyincreases the aerodynamic efficiency of the airfoil 100 (as well as theentire compressor section 14) when compared to prior designs.

In particular, FIG. 5 is a graph of a stagger angle distribution,plotted from 15% to 85% span of an airfoil 100 belonging to a statorvane 50 within the seventeenth stage S17 (i.e., a seventeenth stagestator vane). In some embodiments, all of the stator vanes 50 within theseventeenth stage S17 of the compressor section 14 may include anairfoil 100 having a profile defined by the X, Y, and Z coordinatevalues of TABLE I and the stagger angle distribution according to FIG. 5. The stagger angle distribution shown in FIG. 5 is plotted according tothe points in TABLE III below.

TABLE III Stage Seventeen Stator Vane Airfoil (%) — Span Stagger/MidspanStagger 85.00% 1.133 81.17% 1.088 68.65% 1.000 62.25% 0.989 49.13% 1.00142.48% 1.015 29.16% 1.064 22.53% 1.107 15.00% 1.173

FIG. 6 is a graph of a stagger angle distribution, plotted from 15% to85% span of an airfoil 100 belonging to a stator vane 50 within theeighteenth stage S18 (i.e., an eighteenth stage stator vane). In someembodiments, all of the stator vanes 50 within the eighteenth stage S18of the compressor section 14 may include an airfoil 100 having a profiledefined by the X, Y, and Z coordinate values of TABLE II and the staggerdistribution according to FIG. 6 . The stagger angle distribution shownin FIG. 6 is plotted according to the points in TABLE IV below.

TABLE IV Stage Eighteen Stator Vane Airfoil (%) — Span Stagger/MidspanStagger 85.00% 1.091 81.31% 1.055 68.42% 0.991 61.90% 0.987 48.61% 1.00241.94% 1.016 28.63% 1.065 22.03% 1.106 15.00% 1.164

The disclosed airfoil shape optimizes and is specific to the machineconditions and specifications. It provides a unique profile toachieve 1) interaction between other stages in the compressor section14; 2) aerodynamic efficiency; and 3) normalized aerodynamic andmechanical blade loadings. The disclosed loci of points defined in eachof TABLES I and II allow the gas turbine 10 or any other suitableturbine to run in an efficient, safe and smooth manner. As also noted,the disclosed airfoil 100 may be adapted to any scale, as long as 1)interaction between other stages in the compressor section 14; 2)aerodynamic efficiency; and 3) normalized aerodynamic and mechanicalblade loadings are maintained in the scaled turbine.

The airfoil 100 described herein thus improves overall gas turbine 10efficiency. The airfoil 100 also meets all aeromechanical and stressrequirements. For example, the airfoil 100 of the stator vane 50 thus isof a specific shape to meet aerodynamic, mechanical, and heat transferrequirements in an efficient and cost-effective manner.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they include structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal language of the claims.

Further aspects of the invention are provided by the subject matter ofthe following clauses:

A stator vane comprising: an airfoil having an airfoil shape, theairfoil shape having a nominal profile substantially in accordance withCartesian coordinate values of X, Y, and Z set forth in one of TABLE Ior TABLE II, the Cartesian coordinate values of X, Y, and Z beingdefined relative to a point data origin at a base of the airfoil,wherein the Cartesian coordinate values of X, Y, and Z arenon-dimensional values that are convertible to dimensional distancesexpressed in a unit of distance by multiplying the Cartesian coordinatevalues of X, Y, and Z by a scaling factor of the airfoil in the unit ofdistance; and wherein X and Y values are connected by smooth continuingarcs to define airfoil profile sections at each Z value, the airfoilprofile sections at Z values being joined smoothly with one another toform a complete airfoil shape.

The stator vane of any of the preceding clauses, wherein the airfoilincludes a stagger angle distribution, each stagger angle in the staggerangle distribution being measured between a chord line of the airfoiland a rotary axis of the airfoil; wherein, when the airfoil is definedby the Cartesian coordinate values of X, Y, and Z set forth in TABLE I,the stagger angle distribution is defined in accordance with TABLE III;and wherein, when the airfoil is defined by the Cartesian coordinatevalues of X, Y, and Z set forth in TABLE II, the stagger angledistribution is defined in accordance with TABLE IV.

The stator vane of any of the preceding clauses, wherein the stator vaneforms part of a mid stage of a compressor section.

The stator vane of any of the preceding clauses, wherein the stator vaneis defined by TABLE I and is a seventeenth stage compressor stator vane.

The stator vane of any of the preceding clauses, wherein the stator vaneis defined by TABLE II and is an eighteenth stage compressor statorvane.

The stator vane of any of the preceding clauses, wherein the airfoilshape lies in an envelope within +/−5% of a chord length in a directionnormal to any airfoil surface location.

The stator vane of any of the preceding clauses, wherein the scalingfactor is between about 0.01 inches and about 10 inches.

The stator vane of any of the preceding clauses, wherein the X, Y, and Zvalues are scalable as a function of the same constant or number toprovide a scaled-up or scaled-down airfoil.

A stator vane comprising: an airfoil having a nominal suction-sideprofile substantially in accordance with suction-side Cartesiancoordinate values of X, Y, and Z set forth in one of TABLE I or TABLEII, the Cartesian coordinate values of X, Y, and Z being definedrelative to a point data origin at a base of the airfoil, wherein theCartesian coordinate values of X, Y, and Z are non-dimensional valuesthat are convertible to dimensional distances expressed in a unit ofdistance by multiplying the Cartesian coordinate values of X, Y, and Zby a scaling factor of the airfoil in the unit of distance; and whereinX and Y values are connected by smooth continuing arcs to definesuction-side profile sections at each Z value, the suction-side profilesections at the Z values being joined smoothly with one another to forma complete airfoil suction-side shape.

The stator vane of any of the preceding clauses, wherein the airfoilincludes a stagger angle distribution, each stagger angle in the staggerangle distribution being measured between a chord line of the airfoiland a rotary axis of the airfoil; wherein, when the airfoil has thenominal suction-side profile defined by the Cartesian coordinate valuesof X, Y, and Z set forth in TABLE I, the stagger angle distribution isdefined in accordance with TABLE III; and wherein, when the airfoil hasthe nominal suction-side profile defined by the Cartesian coordinatevalues of X, Y, and Z set forth in TABLE II, the stagger angledistribution is defined in accordance with TABLE IV.

The stator vane any of the preceding clauses, wherein the stator vaneforms part of a mid stage of a compressor section.

The stator vane any of the preceding clauses, wherein the stator vane isdefined by TABLE I and is a seventeenth stage compressor stator vane.

The stator vane of any of the preceding clauses, wherein the stator vaneis defined by TABLE II and is an eighteenth stage compressor statorvane.

The stator vane of any of the preceding clauses, wherein the nominalsuction-side profile lies in an envelope within +/−5% of a chord lengthin a direction normal to any airfoil surface location.

The stator vane of any of the preceding clauses, wherein the scalingfactor is between about 0.01 inches and about 10 inches.

The stator vane of any of the preceding clauses, wherein the X, Y, and Zvalues are scalable as a function of the same constant or number toprovide a scaled-up or scaled-down airfoil.

A turbomachine comprising: a compressor section; a turbine sectiondownstream from the compressor section; a combustion section downstreamfrom the compressor section and upstream from the turbine section; and astator vane disposed within the compressor section, the stator vanecomprising: an airfoil having an airfoil shape, the airfoil shape havinga nominal profile substantially in accordance with Cartesian coordinatevalues of X, Y, and Z set forth in one of TABLE I or TABLE II, theCartesian coordinate values of X, Y, and Z being defined relative to apoint data origin at a base of the airfoil, wherein the Cartesiancoordinate values of X, Y, and Z are non-dimensional values that areconvertible to dimensional distances expressed in a unit of distance bymultiplying the Cartesian coordinate values of X, Y, and Z by a heightof the airfoil in the unit of distance; and wherein X and Y values areconnected by smooth continuing arcs to define airfoil profile sectionsat each Z value, the airfoil profile sections at Z values being joinedsmoothly with one another to form a complete airfoil shape.

The turbomachine of any of the preceding clauses, wherein the airfoilincludes a stagger angle distribution, each stagger angle in the staggerangle distribution being measured between a chord line of the airfoiland a rotary axis of the airfoil; wherein, when the airfoil has thenominal suction-side profile defined by the Cartesian coordinate valuesof X, Y, and Z set forth in TABLE I, the stagger angle distribution isdefined in accordance with TABLE III; and wherein, when the airfoil hasthe nominal suction-side profile defined by the Cartesian coordinatevalues of X, Y, and Z set forth in TABLE II, the stagger angledistribution is defined in accordance with TABLE IV.

What is claimed is:
 1. A stator vane comprising: an airfoil having anairfoil shape, the airfoil shape having a nominal profile substantiallyin accordance with Cartesian coordinate values of X, Y, and Z set forthin one of TABLE I or TABLE II, the Cartesian coordinate values of X, Y,and Z being defined relative to a point data origin at a base of theairfoil, wherein the Cartesian coordinate values of X, Y, and Z arenon-dimensional values that are convertible to dimensional distancesexpressed in a unit of distance by multiplying the Cartesian coordinatevalues of X, Y, and Z by a scaling factor of the airfoil in the unit ofdistance; and wherein X and Y values are connected by smooth continuingarcs to define airfoil profile sections at each Z value, the airfoilprofile sections at Z values being joined smoothly with one another toform a complete airfoil shape.
 2. The stator vane of claim 1, whereinthe airfoil includes a stagger angle distribution, each stagger angle inthe stagger angle distribution being measured between a chord line ofthe airfoil and a rotary axis of the airfoil; wherein, when the airfoilis defined by the Cartesian coordinate values of X, Y, and Z set forthin TABLE I, the stagger angle distribution is defined in accordance withTABLE III; and wherein, when the airfoil is defined by the Cartesiancoordinate values of X, Y, and Z set forth in TABLE II, the staggerangle distribution is defined in accordance with TABLE IV.
 3. The statorvane of claim 1, wherein the stator vane forms part of a mid stage of acompressor section.
 4. The stator vane of claim 3, wherein the statorvane is defined by TABLE I and is a seventeenth stage compressor statorvane.
 5. The stator vane of claim 3, wherein the stator vane is definedby TABLE II and is an eighteenth stage compressor stator vane.
 6. Thestator vane of claim 1, wherein the airfoil shape lies in an envelopewithin +/−5% of a chord length in a direction normal to any airfoilsurface location.
 7. The stator vane of claim 1, wherein the scalingfactor is between about 0.01 inches and about 10 inches.
 8. The statorvane of claim 1, wherein the X, Y, and Z values are scalable as afunction of the same constant or number to provide a scaled-up orscaled-down airfoil.
 9. A stator vane comprising: an airfoil having anominal suction-side profile substantially in accordance withsuction-side Cartesian coordinate values of X, Y, and Z set forth in oneof TABLE I or TABLE II, the Cartesian coordinate values of X, Y, and Zbeing defined relative to a point data origin at a base of the airfoil,wherein the Cartesian coordinate values of X, Y, and Z arenon-dimensional values that are convertible to dimensional distancesexpressed in a unit of distance by multiplying the Cartesian coordinatevalues of X, Y, and Z by a scaling factor of the airfoil in the unit ofdistance; and wherein X and Y values are connected by smooth continuingarcs to define suction-side profile sections at each Z value, thesuction-side profile sections at the Z values being joined smoothly withone another to form a complete airfoil suction-side shape.
 10. Thestator vane of claim 8, wherein the airfoil includes a stagger angledistribution, each stagger angle in the stagger angle distribution beingmeasured between a chord line of the airfoil and a rotary axis of theairfoil; wherein, when the airfoil has the nominal suction-side profiledefined by the Cartesian coordinate values of X, Y, and Z set forth inTABLE I, the stagger angle distribution is defined in accordance withTABLE III; and wherein, when the airfoil has the nominal suction-sideprofile defined by the Cartesian coordinate values of X, Y, and Z setforth in TABLE II, the stagger angle distribution is defined inaccordance with TABLE IV.
 11. The stator vane of claim 9, wherein thestator vane forms part of a mid stage of a compressor section.
 12. Thestator vane of claim 11, wherein the stator vane is defined by TABLE Iand is a seventeenth stage compressor stator vane.
 13. The stator vaneof claim 11, wherein the stator vane is defined by TABLE II and is aneighteenth stage compressor stator vane.
 14. The stator vane of claim 9,wherein the nominal suction-side profile lies in an envelope within+/−5% of a chord length in a direction normal to any airfoil surfacelocation.
 15. The stator vane of claim 9, wherein the scaling factor isbetween about 0.01 inches and about 10 inches.
 16. The stator vane ofclaim 9, wherein the X, Y, and Z values are scalable as a function ofthe same constant or number to provide a scaled-up or scaled-downairfoil.
 17. A turbomachine comprising: a compressor section; a turbinesection downstream from the compressor section; a combustion sectiondownstream from the compressor section and upstream from the turbinesection; and a stator vane disposed within the compressor section, thestator vane comprising: an airfoil having an airfoil shape, the airfoilshape having a nominal profile substantially in accordance withCartesian coordinate values of X, Y, and Z set forth in one of TABLE Ior TABLE II, the Cartesian coordinate values of X, Y, and Z beingdefined relative to a point data origin at a base of the airfoil,wherein the Cartesian coordinate values of X, Y, and Z arenon-dimensional values that are convertible to dimensional distancesexpressed in a unit of distance by multiplying the Cartesian coordinatevalues of X, Y, and Z by a height of the airfoil in the unit ofdistance; and wherein X and Y values are connected by smooth continuingarcs to define airfoil profile sections at each Z value, the airfoilprofile sections at Z values being joined smoothly with one another toform a complete airfoil shape.
 18. The turbomachine of claim 17, whereinthe airfoil includes a stagger angle distribution, each stagger angle inthe stagger angle distribution being measured between a chord line ofthe airfoil and a rotary axis of the airfoil; wherein, when the airfoilhas the nominal suction-side profile defined by the Cartesian coordinatevalues of X, Y, and Z set forth in TABLE I, the stagger angledistribution is defined in accordance with TABLE III; and wherein, whenthe airfoil has the nominal suction-side profile defined by theCartesian coordinate values of X, Y, and Z set forth in TABLE II, thestagger angle distribution is defined in accordance with TABLE IV.